notebooks/1-intro-to-linear-algebra.ipynb

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        "<a href=\"https://colab.research.google.com/github/joanby/matematicas-ml/blob/master/1_intro_to_linear_algebra.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
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    {
      "cell_type": "markdown",
      "metadata": {
        "id": "aTOLgsbN69-P"
      },
      "source": [
        "# Introducción al Álgebra Lineal"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "yqUB9FTRAxd-"
      },
      "source": [
        "Este tema, *Introducción al Álgebra Lineal*, es el primero de la serie *Fundamentos del Aprendizaje Automático*.\n",
        "\n",
        "Es esencial porque el álgebra lineal se encuentra en el corazón de la mayoría de los enfoques de aprendizaje automático y es especialmente predominante en el aprendizaje profundo, la rama de ML a la vanguardia de los avances actuales de inteligencia artificial. A través de la exposición mesurada de la teoría emparejada con ejemplos interactivos, desarrollará una comprensión de cómo se utiliza el álgebra lineal para resolver valores desconocidos en espacios de alta dimensión, lo que permite a las máquinas reconocer patrones y hacer predicciones.\n",
        "\n",
        "El contenido cubierto en *Introducción al Álgebra Lienal* es en sí mismo fundamental para todos los demás temas de la serie Fundamentos Matemáticos del Machine Learning y es especialmente relevante para *Álgebra Lineal II*."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "d4tBvI88BheF"
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      "source": [
        "A lo largo del estudio de este tema, vamos a:\n",
        "\n",
        "* Comprender los fundamentos del álgebra lineal, un enfoque omnipresente para resolver incógnitas dentro de espacios de alta dimensión.\n",
        "* Desarrollar una intuición geométrica de lo que está pasando bajo el capó de los algoritmos de aprendizaje automático, incluidos los utilizados para el aprendizaje profundo.\n",
        "* Ser capaces de comprender más íntimamente los detalles de los documentos de aprendizaje automático, así como todos los demás temas que subyacen ML, incluyendo el cálculo, la estadística y algoritmos de optimización."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Z68nQ0ekCYhF"
      },
      "source": [
        "**Tenga en cuenta que este notebook de Jupyter no está diseñado para ser utilizado solo. Es el código que acompaña a una clase o a los vídeos de la serie [Fundamentos Matemáticos de Machine Learning](https://github.com/joanby/matematicas-ml) de Juan Gabriel Gomila, que ofrecen detalles sobre lo siguiente:**\n",
        "\n",
        "*Segmento 1: Estructuras de datos para álgebra*.\n",
        "\n",
        "* Qué es el álgebra lineal  \n",
        "* Breve historia del álgebra\n",
        "* Tensores\n",
        "* Escalares\n",
        "* Vectores y Transposición de Vectores\n",
        "* Normas y Vectores Unitarios\n",
        "* Vectores Base, Ortogonales y Ortonormales\n",
        "* Matrices en NumPy  \n",
        "* Matrices\n",
        "* Tensores en TensorFlow y PyTorch\n",
        "\n",
        "*Segmento 2: Operaciones Tensoriales Comunes*\n",
        "\n",
        "* Transposición de Tensores\n",
        "* Aritmética Tensorial Básica\n",
        "* Reducción\n",
        "* El Producto Punto\n",
        "* Resolución de sistemas lineales\n",
        "\n",
        "*Segmento 3: Propiedades de las matrices*\n",
        "\n",
        "* La norma de Frobenius\n",
        "* Multiplicación de matrices\n",
        "* Matrices simétricas y matrices identidad\n",
        "* Inversión de matrices\n",
        "* Matrices diagonales\n",
        "* Matrices ortogonales"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "2khww76J5w9n"
      },
      "source": [
        "## Segmento 1: Estructuras de datos para álgebra\n",
        "\n",
        "**Diapositivas utilizadas para comenzar el segmento, con un enfoque en la introducción de lo que es el álgebra lineal, incluyendo ejercicios prácticos de papel y lápiz.**"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "niG_MgK-iV6K"
      },
      "source": [
        "### Qué es Álgebra Lineal"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "LApX90aliab_"
      },
      "source": [
        "import numpy as np\n",
        "import matplotlib.pyplot as plt"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "E4odh9Shic1S"
      },
      "source": [
        "t = np.linspace(0, 40, 1000) # inicio, final, n puntos"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "N-tYny12nIyO"
      },
      "source": [
        "Distancia recorrida por el ladrón: $d = 2.5t$"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "e_zDOxgHiezz"
      },
      "source": [
        "d_r = 2.5 * t"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "djVjXZy-nPaR"
      },
      "source": [
        "Distancia recorrida por el Sheriff: $d = 3(t-5)$"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "JtaNeYSCifrI"
      },
      "source": [
        "d_s = 3 * (t-5)"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "SaaIjJSEigic",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 472
        },
        "outputId": "f795316d-48de-4177-ca97-50a41fa232a0"
      },
      "source": [
        "fig, ax = plt.subplots()\n",
        "plt.title('El Ladrón de Bancos Atrapado')\n",
        "plt.xlabel('tiempo (en minutos)')\n",
        "plt.ylabel('distancia (en km)')\n",
        "ax.set_xlim([0, 40])\n",
        "ax.set_ylim([0, 100])\n",
        "ax.plot(t, d_r, c='green')\n",
        "ax.plot(t, d_s, c='brown')\n",
        "plt.axvline(x=30, color='purple', linestyle='--')\n",
        "_ = plt.axhline(y=75, color='purple', linestyle='--')"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "kpwZw64EYfs6"
      },
      "source": [
        "**Volvemos a las slides.**"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "NgGMhK4B51oe"
      },
      "source": [
        "### Escalares (Tensores de Rango 0) en bases de Python"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "ZXnTHDn_EW6b",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "686d1ca7-9a4b-4593-f70b-93266a90e957"
      },
      "source": [
        "x = 25\n",
        "x"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "25"
            ]
          },
          "metadata": {},
          "execution_count": 5
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "VF8Jam76R4KJ",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "8ca3744b-6efa-4eab-ccbe-00ef7a4a4685"
      },
      "source": [
        "type(x) # si queremos más especificidad (por ejemplo, int16, uint8), necesitamos NumPy u otra librería numérica"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "int"
            ]
          },
          "metadata": {},
          "execution_count": 6
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "ZBzYlL0mRd-P"
      },
      "source": [
        "y = 3"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "1i-hW0bcReyy",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "c18436e4-9d82-4e18-dd5d-1492717e6c9e"
      },
      "source": [
        "py_sum = x + y\n",
        "py_sum"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "28"
            ]
          },
          "metadata": {},
          "execution_count": 8
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "CpyUxB6XRk6y",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "0b4cf197-7a74-408b-ba5c-d4b6ec9babb0"
      },
      "source": [
        "type(py_sum)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "int"
            ]
          },
          "metadata": {},
          "execution_count": 9
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "V2UiLj-JR8Ij",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "a8cc5f6d-bb17-46a5-b566-78ef1fec8019"
      },
      "source": [
        "x_float = 25.0\n",
        "float_sum = x_float + y\n",
        "float_sum"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "28.0"
            ]
          },
          "metadata": {},
          "execution_count": 10
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "ikOwjp6ASCaf",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "24a5f41d-9caa-4ea5-9898-ca3c3a9a6b54"
      },
      "source": [
        "type(float_sum)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "float"
            ]
          },
          "metadata": {},
          "execution_count": 11
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "SgUvioyUz8T2"
      },
      "source": [
        "### Escalares en PyTorch\n",
        "\n",
        "* PyTorch y TensorFlow son las dos librerías de *diferenciación automática* más populares (un foco de los temas [*Cálculo I*](https://github.com/joanby/matematicas-ml/blob/master/notebooks/3-calculus-i.ipynb) y [*Cálculo II*](https://github.com/joanby/matematicas-ml/blob/master/notebooks/4-calculus-ii.ipynb) de la serie *Fundamentos de ML*) en Python, a su vez el lenguaje de programación más popular en ML.\n",
        "* Los tensores de PyTorch están diseñados para ser pitónicos, es decir, para sentirse y comportarse como las matrices de NumPy.\n",
        "* La ventaja de los tensores de PyTorch respecto a los arrays de NumPy es que se pueden usar fácilmente para operaciones en la GPU (ver [aquí](https://pytorch.org/tutorials/beginner/examples_tensor/two_layer_net_tensor.html) por ejemplo).\n",
        "* La documentación sobre los tensores de PyTorch, incluyendo los tipos de datos disponibles, está [aquí](https://pytorch.org/docs/stable/tensors.html)."
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "import torch"
      ],
      "metadata": {
        "id": "ZtXHHhoUHG0x"
      },
      "execution_count": 1,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "a211IRW_0-iY",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "0fd788e5-cc88-4f91-c58a-292a91c2657c"
      },
      "source": [
        "x_pt = torch.tensor(25) # especificación de tipo opcional, por ejemplo: dtype=torch.float16\n",
        "x_pt"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "tensor(25)"
            ]
          },
          "metadata": {},
          "execution_count": 13
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "LvxzMa_HhUNB",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "27ce06b5-ea7b-4f6c-c57e-9a7f88f39f5f"
      },
      "source": [
        "x_pt.shape"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "torch.Size([])"
            ]
          },
          "metadata": {},
          "execution_count": 14
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "eUyuZXlWS8T9"
      },
      "source": [
        "### Escalares en TensorFlow (versión 2.0 o posterior)\n",
        "\n",
        "Tensores creados con una envoltura, todo lo cual [se puede leer aquí](https://www.tensorflow.org/guide/tensor):  \n",
        "\n",
        "* `tf.Variable`\n",
        "* `tf.constant`\n",
        "* `tf.placeholder`\n",
        "* `tf.SparseTensor`\n",
        "\n",
        "El más utilizado es `tf.Variable`, que usaremos aquí.\n",
        "\n",
        "Al igual que con los tensores TF, en PyTorch podemos realizar operaciones similares, y podemos convertir fácilmente a y desde arrays NumPy.\n",
        "\n",
        "Además, una lista completa de los tipos de datos de los tensores está disponible [aquí](https://www.tensorflow.org/api_docs/python/tf/dtypes/DType)."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "CHBYse_MEqZM"
      },
      "source": [
        "import tensorflow as tf"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "sDv92Nh-NSOU",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "c8b0997b-d19a-4616-db95-9dbafe291444"
      },
      "source": [
        "x_tf = tf.Variable(25, dtype=tf.int16) # dtype es opcional\n",
        "x_tf"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<tf.Variable 'Variable:0' shape=() dtype=int16, numpy=25>"
            ]
          },
          "metadata": {},
          "execution_count": 16
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "EmPMBIV9RQjS",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "985f8db7-a571-4059-8f14-926e694fcff6"
      },
      "source": [
        "x_tf.shape"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "TensorShape([])"
            ]
          },
          "metadata": {},
          "execution_count": 17
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "mEILtO9pPctO"
      },
      "source": [
        "y_tf = tf.Variable(3, dtype=tf.int16)"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "dvvWuaw6Ph_D",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "719913e0-58c7-4bc6-9fcc-ab658a11acbc"
      },
      "source": [
        "x_tf + y_tf"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<tf.Tensor: shape=(), dtype=int16, numpy=28>"
            ]
          },
          "metadata": {},
          "execution_count": 19
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "JZVhRnX9RUGW",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "4c80996f-6259-460e-e5d2-f66e63718a52"
      },
      "source": [
        "tf_sum = tf.add(x_tf, y_tf)\n",
        "tf_sum"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<tf.Tensor: shape=(), dtype=int16, numpy=28>"
            ]
          },
          "metadata": {},
          "execution_count": 20
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "sVbMxT1Ey6Y3",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "4fcbcaa3-855d-487b-cdbe-23efa6f2fc53"
      },
      "source": [
        "tf_sum.numpy() # veamos que las operaciones NumPy convierten automáticamente los tensores en matrices NumPy, y viceversa"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "28"
            ]
          },
          "metadata": {},
          "execution_count": 21
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "LXpv69t0y-f6",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "52c8c0e4-4157-439d-a337-07b2d1f47860"
      },
      "source": [
        "type(tf_sum.numpy())"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "numpy.int16"
            ]
          },
          "metadata": {},
          "execution_count": 22
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "VszuTUAg1uXk",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "94cd1dee-af70-4454-f18c-9e496c5138f6"
      },
      "source": [
        "tf_float = tf.Variable(25., dtype=tf.float16)\n",
        "tf_float"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<tf.Variable 'Variable:0' shape=() dtype=float16, numpy=25.0>"
            ]
          },
          "metadata": {},
          "execution_count": 23
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "B5VRGo1H6010"
      },
      "source": [
        "**Vovlemos a las slides aquí.**"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "4CURG9Er6aZI"
      },
      "source": [
        "### Vectores (Tensores de rango 1) en NumPy"
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "import numpy as np"
      ],
      "metadata": {
        "id": "XRFB5UprKZwb"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "T9ME4kBr4wg0",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "bf807ca5-344c-407f-f58a-e49c7c3e5a12"
      },
      "source": [
        "x = np.array([25, 2, 5]) # el parámetro type es opcional, p.ej.: dtype=np.float16\n",
        "x"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([25,  2,  5])"
            ]
          },
          "metadata": {},
          "execution_count": 2
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "ZuotxmlZL2wp",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "482c7cb4-2c72-40f7-e797-6f181dfc1441"
      },
      "source": [
        "len(x)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "3"
            ]
          },
          "metadata": {},
          "execution_count": 26
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "OlPYy6GOaIVy",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "4fac64fb-13da-4f38-8880-fbc9e791ba06"
      },
      "source": [
        "x.shape"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "(3,)"
            ]
          },
          "metadata": {},
          "execution_count": 27
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "sWbYGwObcgtK",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "eaddcd4e-fb43-464d-c100-6329bbdeb590"
      },
      "source": [
        "type(x)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "numpy.ndarray"
            ]
          },
          "metadata": {},
          "execution_count": 28
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "ME_xuvD_oTPg",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "643eecc1-7379-4729-da00-515042ba9dd0"
      },
      "source": [
        "x[0] # zero-indexed"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "25"
            ]
          },
          "metadata": {},
          "execution_count": 29
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "hXmBHZQ-nxFw",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "1be5570a-282c-4454-a0a4-3a265c380db8"
      },
      "source": [
        "type(x[0])"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "numpy.int64"
            ]
          },
          "metadata": {},
          "execution_count": 30
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "NiEofCzYZBrQ"
      },
      "source": [
        "### Transposición de Vectores"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "hxGFNDx6V95l",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "d5dd0100-56dc-46ad-c3dd-1b2549dcaa39"
      },
      "source": [
        "# Transponer un array 1-D normal no tiene ningún efecto...\n",
        "x_t = x.T\n",
        "x_t"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([25,  2,  5])"
            ]
          },
          "metadata": {},
          "execution_count": 31
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "_f8E9ExDWw4p",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "13974b08-8ba0-4c57-caf4-a53e01fa2d4a"
      },
      "source": [
        "x_t.shape"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "(3,)"
            ]
          },
          "metadata": {},
          "execution_count": 32
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "AEd8jB7YcgtT",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "d0b4a0a4-5626-4eef-9051-853f6af3ced5"
      },
      "source": [
        "# ...pero sí cuando utilizamos paréntesis anidados «tipo matriz»:\n",
        "y = np.array([[25, 2, 5]])\n",
        "y"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[25,  2,  5]])"
            ]
          },
          "metadata": {},
          "execution_count": 33
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "UHQd92oRcgtV",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "126fe19f-b4b0-48af-90bd-e31de9123c40"
      },
      "source": [
        "y.shape"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "(1, 3)"
            ]
          },
          "metadata": {},
          "execution_count": 34
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "SPi1JqGEXXUc",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "d136d260-bdf2-4c54-956d-2a35cb978c6f"
      },
      "source": [
        "# ...pero se puede transponer una matriz de dimensión 1, lo que equivale matemáticamente a:\n",
        "y_t = y.T\n",
        "y_t"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[25],\n",
              "       [ 2],\n",
              "       [ 5]])"
            ]
          },
          "metadata": {},
          "execution_count": 35
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "6rzUv762Yjis",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "8abc338f-2adc-4915-8728-c5e76fccfa0e"
      },
      "source": [
        "y_t.shape # Esto es un vector columna ya que tiene 3 filas y 1 columna"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "(3, 1)"
            ]
          },
          "metadata": {},
          "execution_count": 36
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "xVnQMLOrYtra",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "29d42035-3570-4604-e0c7-a861ef3f1eca"
      },
      "source": [
        "# El vector columna puede transponerse al vector fila original:\n",
        "y_t.T"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[25,  2,  5]])"
            ]
          },
          "metadata": {},
          "execution_count": 37
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "QIAA2NLRZIXC",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "e7493ff0-7cd9-4f13-caa3-71c914dbdabe"
      },
      "source": [
        "y_t.T.shape"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "(1, 3)"
            ]
          },
          "metadata": {},
          "execution_count": 38
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Voj26mSpZLuh"
      },
      "source": [
        "### Vectores nulos\n",
        "\n",
        "No tienen efecto si se suman a otro vector"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "-46AbOdkZVn_",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "de2e79d6-217a-4246-fe6c-ea9c12619af2"
      },
      "source": [
        "z = np.zeros(3)\n",
        "z"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([0., 0., 0.])"
            ]
          },
          "metadata": {},
          "execution_count": 39
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "c6xyYiwSnSGC"
      },
      "source": [
        "### Vectores en PyTorch y TensorFlow"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "s2TGDeqXnitZ",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "98da7b38-3727-4c86-aa04-393c5b1fb0c8"
      },
      "source": [
        "x_pt = torch.tensor([25, 2, 5])\n",
        "x_pt"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "tensor([25,  2,  5])"
            ]
          },
          "metadata": {},
          "execution_count": 5
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "-0jbHgc5iijG",
        "scrolled": true,
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "7eb702e8-7e61-47cf-fc8e-acb9dd913b3c"
      },
      "source": [
        "x_tf = tf.Variable([25, 2, 5])\n",
        "x_tf"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<tf.Variable 'Variable:0' shape=(3,) dtype=int32, numpy=array([25,  2,  5], dtype=int32)>"
            ]
          },
          "metadata": {},
          "execution_count": 6
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "rTDDta1Ro4Pf"
      },
      "source": [
        "**Volver a las slides aquí.**"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "8fU5qVTI6SLD"
      },
      "source": [
        "### Norma $L^2$"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "lLc2FbGG6SLD",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "d25dd1d1-3fcd-4b38-9e96-3a54e1a6e088"
      },
      "source": [
        "x"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([25,  2,  5])"
            ]
          },
          "metadata": {},
          "execution_count": 42
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "AN43hsl86SLG",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "4fe083bd-0f25-421a-a7d7-2c0c81a2d3c9"
      },
      "source": [
        "(25**2 + 2**2 + 5**2)**(1/2)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "25.573423705088842"
            ]
          },
          "metadata": {},
          "execution_count": 43
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "D9CyWo-l6SLI",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "b43dc5bf-c341-465a-c8df-78b2a6735830"
      },
      "source": [
        "np.linalg.norm(x)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "25.573423705088842"
            ]
          },
          "metadata": {},
          "execution_count": 44
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "TNEMRi926SLK"
      },
      "source": [
        "Así, si las unidades en este espacio vectorial tridimensional son metros, entonces el vector $x$ tiene una longitud de 25.6m"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "ugQC6k4h6SLK"
      },
      "source": [
        "**Volver a las slides aquí.**"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "PwiRlMuC6SLK"
      },
      "source": [
        "### Norma $L^1$"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "lcYKyc5H6SLL",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "d1c2301e-0cee-4e6a-dde0-f9dce5c9bdb5"
      },
      "source": [
        "x"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([25,  2,  5])"
            ]
          },
          "metadata": {},
          "execution_count": 45
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "8jNb6nYl6SLM",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "e7666a62-2680-408e-99f9-7ff4342d0ace"
      },
      "source": [
        "np.abs(25) + np.abs(2) + np.abs(5)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "32"
            ]
          },
          "metadata": {},
          "execution_count": 46
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "WTPz0EBSAVee"
      },
      "source": [
        "**Volver a las slides aquí.**"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "lQP73B916SLP"
      },
      "source": [
        "### Norma $L^2$ al Cuadrado"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "Qv1ouJ8r6SLP",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "e40a1a99-99f7-4901-96f7-97bd91b68cc6"
      },
      "source": [
        "x"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([25,  2,  5])"
            ]
          },
          "metadata": {},
          "execution_count": 47
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "eG3WSB5R6SLT",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "2e94a288-d3f6-4153-f970-b3a853b040d7"
      },
      "source": [
        "(25**2 + 2**2 + 5**2)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "654"
            ]
          },
          "metadata": {},
          "execution_count": 48
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "bXwzSudS6SLV",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "b7cbf5e0-a758-47a3-99ab-51bc28246ac3"
      },
      "source": [
        "# Cubriremos la multiplicación tensorial más pronto pero para probar el producto escalar rápidamente:\n",
        "np.dot(x, x)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "654"
            ]
          },
          "metadata": {},
          "execution_count": 49
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "q3CIH9ba6SLX"
      },
      "source": [
        "**Volver a las slides aquí.**"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "BHWxVPFC6SLX"
      },
      "source": [
        "### Norma del Máximo"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "vO-zfvDG6SLX",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "d08ee1d2-f8ad-4596-abc4-92ec4293ab66"
      },
      "source": [
        "x"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([25,  2,  5])"
            ]
          },
          "metadata": {},
          "execution_count": 50
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "vXXLgbyW6SLZ",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "eaa5cc2d-227b-4fa5-d85b-5e93dce14d68"
      },
      "source": [
        "np.max([np.abs(25), np.abs(2), np.abs(5)])"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "25"
            ]
          },
          "metadata": {},
          "execution_count": 51
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "3MVTsXA8nNR0"
      },
      "source": [
        "**Volver a las slides aquí.**"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "JzKlIpYZcgt9"
      },
      "source": [
        "### Vectores Ortogonales"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "4jHg9La-cgt9",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "e516c0be-543c-4bea-c1d3-a8019e9e0c55"
      },
      "source": [
        "i = np.array([1, 0])\n",
        "i"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([1, 0])"
            ]
          },
          "metadata": {},
          "execution_count": 4
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "3FyLhPK3cguA",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "5797b1af-fe8e-4b99-b725-c279a73b46ee"
      },
      "source": [
        "j = np.array([0, 1])\n",
        "j"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([0, 1])"
            ]
          },
          "metadata": {},
          "execution_count": 5
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "7eQtKhaDcguC",
        "scrolled": false,
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "9a7d3d96-131c-4abd-e7e3-82323b7e64ac"
      },
      "source": [
        "np.dot(i, j) # detalles en el producto escalar próximamente..."
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "0"
            ]
          },
          "metadata": {},
          "execution_count": 6
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "C6eMVPu4nNR7"
      },
      "source": [
        "**Volver a las slides aquí.**"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "mK3AZH53o8Br"
      },
      "source": [
        "### Matrices (Tensores de Rango 2) en NumPy"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "stk57cmaESW1",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "be5e1e27-382c-4d56-c4e9-27f83c303e8f"
      },
      "source": [
        "# Usamos array() con corchetes anidados:\n",
        "X = np.array([[25, 2], [5, 26], [3, 7]])\n",
        "X"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[25,  2],\n",
              "       [ 5, 26],\n",
              "       [ 3,  7]])"
            ]
          },
          "metadata": {},
          "execution_count": 2
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "IhDL4L8S6SLc",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "2e4e097b-fb2f-41e3-dbbe-0b5ac0fb0a69"
      },
      "source": [
        "X.shape"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "(3, 2)"
            ]
          },
          "metadata": {},
          "execution_count": 8
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "q3oyaAK36SLe",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "e7d932a0-e8b7-4eb5-e0c9-0ea8d80997ae"
      },
      "source": [
        "X.size"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "6"
            ]
          },
          "metadata": {},
          "execution_count": 9
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "YN9CHzja6SLg",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "b763dd95-34b4-4517-9678-f3c2b0628938"
      },
      "source": [
        "# Seleccionamos la columna izquierda de la matriz X (índice cero)\n",
        "X[:,0]"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([25,  5,  3])"
            ]
          },
          "metadata": {},
          "execution_count": 10
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "ih7nh4qC6SLi",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "297bc68d-a2fb-4cf4-d7fd-6b11cca6bc04"
      },
      "source": [
        "# Seleccionamos la fila del medio de la matriz:\n",
        "X[1,:]"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([ 5, 26])"
            ]
          },
          "metadata": {},
          "execution_count": 11
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "pg7numxP6SLl",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "5be6e5e8-ab42-4ac2-ac79-e4fdafe6d1ea"
      },
      "source": [
        "# Otro ejemplo de slicing-by-index:\n",
        "X[0:2, 0:2]"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[25,  2],\n",
              "       [ 5, 26]])"
            ]
          },
          "metadata": {},
          "execution_count": 12
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "HGEfZiBb6SLt"
      },
      "source": [
        "### Matrices en PyTorch"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "-bibT9ye6SLt",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "939f3751-745f-4bfb-9b48-60672c3d7b6c"
      },
      "source": [
        "X_pt = torch.tensor([[25, 2], [5, 26], [3, 7]])\n",
        "X_pt"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "tensor([[25,  2],\n",
              "        [ 5, 26],\n",
              "        [ 3,  7]])"
            ]
          },
          "metadata": {},
          "execution_count": 5
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "TBPu1L7P6SLv",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "418bc531-415a-4383-86dc-329edff03f5a"
      },
      "source": [
        "X_pt.shape # pythonico relativo a PyTorch"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "torch.Size([3, 2])"
            ]
          },
          "metadata": {},
          "execution_count": 14
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "4mTj56M16SLw",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "93387222-41e5-412d-a5f8-092036e965ca"
      },
      "source": [
        "X_pt[1,:] # N.B.: Python se basa en índices que empiezan en cero; el álgebra se basa en índice que empieza en 1"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "tensor([ 5, 26])"
            ]
          },
          "metadata": {},
          "execution_count": 15
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "E026fQlD6SLn"
      },
      "source": [
        "### Matrices en TensorFlow"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "1gtGH6oA6SLn",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "7ec30099-7a05-40b9-b8d8-a41ca6c248b2"
      },
      "source": [
        "X_tf = tf.Variable([[25, 2], [5, 26], [3, 7]])\n",
        "X_tf"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<tf.Variable 'Variable:0' shape=(3, 2) dtype=int32, numpy=\n",
              "array([[25,  2],\n",
              "       [ 5, 26],\n",
              "       [ 3,  7]], dtype=int32)>"
            ]
          },
          "metadata": {},
          "execution_count": 6
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "4CV_KiTP6SLp",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "e725df1f-8470-4f1c-9a2d-6eb8819c90ad"
      },
      "source": [
        "tf.rank(X_tf)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<tf.Tensor: shape=(), dtype=int32, numpy=2>"
            ]
          },
          "metadata": {},
          "execution_count": 17
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "vUsce8tC6SLq",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "021f9b48-f32d-4f45-9f23-185d6704c7c6"
      },
      "source": [
        "tf.shape(X_tf)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<tf.Tensor: shape=(2,), dtype=int32, numpy=array([3, 2], dtype=int32)>"
            ]
          },
          "metadata": {},
          "execution_count": 18
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "QNpfvNPj6SLr",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "f9d46348-17c7-45f3-8837-7623c5220c15"
      },
      "source": [
        "X_tf[1,:]"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<tf.Tensor: shape=(2,), dtype=int32, numpy=array([ 5, 26], dtype=int32)>"
            ]
          },
          "metadata": {},
          "execution_count": 19
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "CodS4evY6SLy"
      },
      "source": [
        "**Voler a las slides aquí.**"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "cMpfujF_6SLy"
      },
      "source": [
        "### Tensores de Rango Superior\n",
        "\n",
        "Como ejemplo, los tensores de rango 4 son comunes para las imágenes, donde cada dimensión corresponde a:\n",
        "\n",
        "1. Número de imágenes en el lote de entrenamiento, por ejemplo, 32\n",
        "2. Altura de la imagen en píxeles, por ejemplo, 28 para [MNIST digits](http://yann.lecun.com/exdb/mnist/)\n",
        "3. Anchura de la imagen en píxeles, p. ej., 28\n",
        "4. Número de canales de color, por ejemplo, 3 para imágenes a todo color (RGB)"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "KSZlICRR6SL1"
      },
      "source": [
        "images_pt = torch.zeros([32, 28, 28, 3])"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "6Dqj0vmh6SL2",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "c1ba21d3-674f-4f06-a7c8-6e8123a69e4d"
      },
      "source": [
        "# images_pt"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "tensor([[[[0., 0., 0.],\n",
              "          [0., 0., 0.],\n",
              "          [0., 0., 0.],\n",
              "          ...,\n",
              "          [0., 0., 0.],\n",
              "          [0., 0., 0.],\n",
              "          [0., 0., 0.]],\n",
              "\n",
              "         [[0., 0., 0.],\n",
              "          [0., 0., 0.],\n",
              "          [0., 0., 0.],\n",
              "          ...,\n",
              "          [0., 0., 0.],\n",
              "          [0., 0., 0.],\n",
              "          [0., 0., 0.]],\n",
              "\n",
              "         [[0., 0., 0.],\n",
              "          [0., 0., 0.],\n",
              "          [0., 0., 0.],\n",
              "          ...,\n",
              "          [0., 0., 0.],\n",
              "          [0., 0., 0.],\n",
              "          [0., 0., 0.]],\n",
              "\n",
              "         ...,\n",
              "\n",
              "         [[0., 0., 0.],\n",
              "          [0., 0., 0.],\n",
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              "          ...,\n",
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              "          ...,\n",
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              "\n",
              "         ...,\n",
              "\n",
              "         [[0., 0., 0.],\n",
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              "          ...,\n",
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              "\n",
              "         [[0., 0., 0.],\n",
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              "          ...,\n",
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              "          [0., 0., 0.]],\n",
              "\n",
              "         [[0., 0., 0.],\n",
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              "          ...,\n",
              "          [0., 0., 0.],\n",
              "          [0., 0., 0.],\n",
              "          [0., 0., 0.]]]])"
            ]
          },
          "metadata": {},
          "execution_count": 21
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "7TASTVD96SLy"
      },
      "source": [
        "images_tf = tf.zeros([32, 28, 28, 3])"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "ftOliyru6SL0",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "653afc1a-26af-450a-a61f-9316b2ec8cfb"
      },
      "source": [
        "# images_tf"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
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              "         ...,\n",
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              "         ...,\n",
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              "\n",
              "\n",
              "       [[[0., 0., 0.],\n",
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              "         [0., 0., 0.],\n",
              "         ...,\n",
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              "        [[0., 0., 0.],\n",
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              "         ...,\n",
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              "\n",
              "        [[0., 0., 0.],\n",
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              "         ...,\n",
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              "\n",
              "        ...,\n",
              "\n",
              "        [[0., 0., 0.],\n",
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              "         [0., 0., 0.],\n",
              "         ...,\n",
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              "         [0., 0., 0.]],\n",
              "\n",
              "        [[0., 0., 0.],\n",
              "         [0., 0., 0.],\n",
              "         [0., 0., 0.],\n",
              "         ...,\n",
              "         [0., 0., 0.],\n",
              "         [0., 0., 0.],\n",
              "         [0., 0., 0.]],\n",
              "\n",
              "        [[0., 0., 0.],\n",
              "         [0., 0., 0.],\n",
              "         [0., 0., 0.],\n",
              "         ...,\n",
              "         [0., 0., 0.],\n",
              "         [0., 0., 0.],\n",
              "         [0., 0., 0.]]]], dtype=float32)>"
            ]
          },
          "metadata": {},
          "execution_count": 23
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "O3sgkdXZ6SL3"
      },
      "source": [
        "**Volver a las slides aquí.**"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "lmG3LEZK6SL4"
      },
      "source": [
        "## Segmento 2: Operaciones con Tensores más comunes"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "iSHGMCxd6SL4"
      },
      "source": [
        "### Transposición de Tensores"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "1YN1narR6SL4",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "33c08cda-07b3-4b8b-882d-589b296835fe"
      },
      "source": [
        "X"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[25,  2],\n",
              "       [ 5, 26],\n",
              "       [ 3,  7]])"
            ]
          },
          "metadata": {},
          "execution_count": 3
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "5hf3M_NL6SL5",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "2442c6a7-f6f6-409b-b208-f129a2ea1ba9"
      },
      "source": [
        "X.T"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[25,  5,  3],\n",
              "       [ 2, 26,  7]])"
            ]
          },
          "metadata": {},
          "execution_count": 4
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "vyBFN_4g6SL9",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "3a7de82e-97a9-44af-b435-d91e6fa9d725"
      },
      "source": [
        "X_pt.T"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "tensor([[25,  5,  3],\n",
              "        [ 2, 26,  7]])"
            ]
          },
          "metadata": {},
          "execution_count": 7
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "K2DuDJc_6SL6",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "523c1fb0-fd83-4731-cbb1-50cee99aacbe"
      },
      "source": [
        "tf.transpose(X_tf) # menos Pythonico"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<tf.Tensor: shape=(2, 3), dtype=int32, numpy=\n",
              "array([[25,  5,  3],\n",
              "       [ 2, 26,  7]], dtype=int32)>"
            ]
          },
          "metadata": {},
          "execution_count": 8
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Hp9P1jx76SL_"
      },
      "source": [
        "### Propiedades Aritméticas Básicas\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "WxaImEUc6SMA"
      },
      "source": [
        "Al sumar o multiplicar con escalares se aplica la operación a todos los elementos y se conserva la forma del tensor:"
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "X"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "SYaGPcnQl5Hu",
        "outputId": "2b22067b-ee90-4f55-9332-44809e49ccf0"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[25,  2],\n",
              "       [ 5, 26],\n",
              "       [ 3,  7]])"
            ]
          },
          "metadata": {},
          "execution_count": 9
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "yhXGETii6SMA",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "84702145-5cd9-4e2a-c10b-f69f94fc9ff6"
      },
      "source": [
        "X*2"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[50,  4],\n",
              "       [10, 52],\n",
              "       [ 6, 14]])"
            ]
          },
          "metadata": {},
          "execution_count": 10
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "KnPULtDO6SMC",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "062036ec-d3de-45f9-cea0-63ea630d5b28"
      },
      "source": [
        "X+2"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[27,  4],\n",
              "       [ 7, 28],\n",
              "       [ 5,  9]])"
            ]
          },
          "metadata": {},
          "execution_count": 11
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "MkfC0Gsb6SMD",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "75d61e95-26dc-46f4-ac93-117939bfbcf7"
      },
      "source": [
        "X*2+2"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[52,  6],\n",
              "       [12, 54],\n",
              "       [ 8, 16]])"
            ]
          },
          "metadata": {},
          "execution_count": 12
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "04bIDpGj6SMH",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "0a924ec4-488d-4e44-b5f4-321238cd0288"
      },
      "source": [
        "X_pt*2+2 # Los operadores de Python están sobrecargados; también podemos utilizar torch.mul() o torch.add()"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "tensor([[52,  6],\n",
              "        [12, 54],\n",
              "        [ 8, 16]])"
            ]
          },
          "metadata": {},
          "execution_count": 13
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "2oRBSmRL6SMI",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "5b38ef16-6d75-4e05-b19c-0cd24c9d6347"
      },
      "source": [
        "torch.add(torch.mul(X_pt, 2), 2)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "tensor([[52,  6],\n",
              "        [12, 54],\n",
              "        [ 8, 16]])"
            ]
          },
          "metadata": {},
          "execution_count": 14
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "OMSb9Otd6SMF",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "a72a69fb-304c-48df-b5a1-7f46b8552f4a"
      },
      "source": [
        "X_tf*2+2 # Operadores igualmente sobrecargados; podríamos utilizar igualmente tf.multiply() tf.add()"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<tf.Tensor: shape=(3, 2), dtype=int32, numpy=\n",
              "array([[52,  6],\n",
              "       [12, 54],\n",
              "       [ 8, 16]], dtype=int32)>"
            ]
          },
          "metadata": {},
          "execution_count": 15
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "5ya2xZ4u6SMG",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "a311cec1-310e-4de6-8322-942bf6206baf"
      },
      "source": [
        "tf.add(tf.multiply(X_tf, 2), 2)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<tf.Tensor: shape=(3, 2), dtype=int32, numpy=\n",
              "array([[52,  6],\n",
              "       [12, 54],\n",
              "       [ 8, 16]], dtype=int32)>"
            ]
          },
          "metadata": {},
          "execution_count": 16
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "wt8Ls4076SMK"
      },
      "source": [
        "Si dos tensores tienen el mismo tamaño, las operaciones se suelen aplicar por defecto de forma elemental. No se trata de **multiplicación de matrices**, que veremos más adelante, sino que se denomina **producto de Hadamard** o simplemente **producto elemento a elemento**.\n",
        "\n",
        "La notación matemática es $A \\odot X$."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "KUMyU1t46SMK",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "55db7359-3648-47c4-8b56-45000d53f3fb"
      },
      "source": [
        "X"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[25,  2],\n",
              "       [ 5, 26],\n",
              "       [ 3,  7]])"
            ]
          },
          "metadata": {},
          "execution_count": 17
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "UNIbp0P36SML",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "bb78527a-cf48-4f75-a1d7-577b9f30b37b"
      },
      "source": [
        "A = X+2\n",
        "A"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[27,  4],\n",
              "       [ 7, 28],\n",
              "       [ 5,  9]])"
            ]
          },
          "metadata": {},
          "execution_count": 18
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "HE9xPWPdcgu4",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "fcd25416-ccef-491d-aa77-9c5db729aa58"
      },
      "source": [
        "A + X"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[52,  6],\n",
              "       [12, 54],\n",
              "       [ 8, 16]])"
            ]
          },
          "metadata": {},
          "execution_count": 19
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "xKyCwGia6SMP",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "66a971db-0423-4f72-9763-eee5ef643c19"
      },
      "source": [
        "A * X"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[675,   8],\n",
              "       [ 35, 728],\n",
              "       [ 15,  63]])"
            ]
          },
          "metadata": {},
          "execution_count": 20
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "B5jXGIBp6SMT"
      },
      "source": [
        "A_pt = X_pt + 2"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "A7k6yxu36SMU",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "f2c3eb53-93ae-4fe7-abff-9a21a04b9011"
      },
      "source": [
        "A_pt + X_pt"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "tensor([[52,  6],\n",
              "        [12, 54],\n",
              "        [ 8, 16]])"
            ]
          },
          "metadata": {},
          "execution_count": 22
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "r8vOul0m6SMW",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "2febfa43-038b-4835-888d-fd70c4251a69"
      },
      "source": [
        "A_pt * X_pt"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "tensor([[675,   8],\n",
              "        [ 35, 728],\n",
              "        [ 15,  63]])"
            ]
          },
          "metadata": {},
          "execution_count": 23
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "rQcBMSb76SMQ"
      },
      "source": [
        "A_tf = X_tf + 2"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "x6s1wtNj6SMR",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "5c2d7839-ef0f-40d9-fdc5-8bf99a2960e7"
      },
      "source": [
        "A_tf + X_tf"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<tf.Tensor: shape=(3, 2), dtype=int32, numpy=\n",
              "array([[52,  6],\n",
              "       [12, 54],\n",
              "       [ 8, 16]], dtype=int32)>"
            ]
          },
          "metadata": {},
          "execution_count": 25
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "J1D7--296SMS",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "4d99995a-ecf2-4a5a-f1d8-ef3f73efe44a"
      },
      "source": [
        "A_tf * X_tf"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<tf.Tensor: shape=(3, 2), dtype=int32, numpy=\n",
              "array([[675,   8],\n",
              "       [ 35, 728],\n",
              "       [ 15,  63]], dtype=int32)>"
            ]
          },
          "metadata": {},
          "execution_count": 26
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "FE5f-FEq6SMY"
      },
      "source": [
        "### Reducción"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "WPJ9FVQF6SMY"
      },
      "source": [
        "Calcular la suma de todos los elementos de un tensor es una operación habitual. Por ejemplo:\n",
        "\n",
        "* Para un vector ***x*** de longitud *n*, calculamos $\\sum_{i=1}^{n} x_i$.\n",
        "* Para la matriz ***X*** con *m* por *n* dimensiones, calculamos $\\sum_{i=1}^{m} \\sum_{j=1}^{n} X_{i,j}$"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "rXi2stvz6SMZ",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "ee1daeec-2af6-463e-8f59-7bf0383f3f32"
      },
      "source": [
        "X"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[25,  2],\n",
              "       [ 5, 26],\n",
              "       [ 3,  7]])"
            ]
          },
          "metadata": {},
          "execution_count": 27
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "W9FKaJbf6SMZ",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "96670a1c-f0fa-4b44-9845-4b38c6295300"
      },
      "source": [
        "X.sum()"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "68"
            ]
          },
          "metadata": {},
          "execution_count": 28
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "3y9aw7t66SMc",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "498b6985-3088-49a1-c846-11d2ef4e9711"
      },
      "source": [
        "torch.sum(X_pt)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "tensor(68)"
            ]
          },
          "metadata": {},
          "execution_count": 29
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "wcjRtFml6SMb",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "ce351854-7eb5-41a9-9103-b700b26130a4"
      },
      "source": [
        "tf.reduce_sum(X_tf)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<tf.Tensor: shape=(), dtype=int32, numpy=68>"
            ]
          },
          "metadata": {},
          "execution_count": 30
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "awjH9bOz6SMc",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "6e6444a5-14e6-4f21-8711-bed928ca14a4"
      },
      "source": [
        "# También puede hacerse a lo largo de un solo eje específico, por ejemplo:\n",
        "X.sum(axis=0) # sumar sobre todas las filas"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([33, 35])"
            ]
          },
          "metadata": {},
          "execution_count": 31
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "n2SASjsn6SMd",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "08d4ff25-cf7f-47d0-bb2e-8e2509784f8a"
      },
      "source": [
        "X.sum(axis=1) # sumar sobre todas las columnas"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([27, 31, 10])"
            ]
          },
          "metadata": {},
          "execution_count": 32
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "uVnSxvSJ6SMh",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "ffadc913-006f-4116-a589-ca129cc25abf"
      },
      "source": [
        "torch.sum(X_pt, 0)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "tensor([33, 35])"
            ]
          },
          "metadata": {},
          "execution_count": 33
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "IO8drxz36SMe",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "a0056725-45fe-4537-c5a1-3926e94feeb2"
      },
      "source": [
        "tf.reduce_sum(X_tf, 1)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<tf.Tensor: shape=(3,), dtype=int32, numpy=array([27, 31, 10], dtype=int32)>"
            ]
          },
          "metadata": {},
          "execution_count": 34
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "gdAe8S4A6SMj"
      },
      "source": [
        "Pueden aplicarse muchas otras operaciones con reducción a lo largo de todos los ejes o de una selección de ellos, p. ej:\n",
        "\n",
        "* máximo\n",
        "* mínimo\n",
        "* media\n",
        "* producto\n",
        "\n",
        "Son bastante sencillas y se utilizan con menos frecuencia que la suma, así que te invitamos a buscarlas en los documentos de la biblioteca si alguna vez las necesitas."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "r2eW8S_46SMj"
      },
      "source": [
        "### El Producto Escalar"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "LImETgD76SMj"
      },
      "source": [
        "Si tenemos dos vectores (digamos, ***x*** y ***y***) con la misma longitud *n*, podemos calcular el producto punto entre ellos. Esto se anota de varias maneras diferentes, incluyendo las siguientes:\n",
        "\n",
        "* $x \\cdot y$\n",
        "* $x^Ty$\n",
        "* $\\langle x,y \\rangle$.\n",
        "\n",
        "Independientemente de la notación que utilices (yo prefiero la primera), el cálculo es el mismo; calculamos los productos de una manera elemento a elemento y luego sumamos reductivamente a través de los productos a un valor escalar. Es decir, $x \\cdot y = \\sum_{i=1}^{n} x_i y_i$.\n",
        "\n",
        "El producto punto es omnipresente en el aprendizaje profundo: Se realiza en cada neurona artificial de una red neuronal profunda, que puede estar formada por millones (u órdenes de magnitud superiores) de estas neuronas."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "HveIE3IDcgvP",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "5172dc25-972d-4366-8147-8e9bf257886b"
      },
      "source": [
        "x"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([25,  2,  5])"
            ]
          },
          "metadata": {},
          "execution_count": 7
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "3ZjkZcvVcgvQ",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "a9ca6376-696b-4cc4-f77d-1fb5da9cb523"
      },
      "source": [
        "y = np.array([0, 1, 2])\n",
        "y"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([0, 1, 2])"
            ]
          },
          "metadata": {},
          "execution_count": 8
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "Xu8z0QB0cgvR",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "6b565ec2-e1eb-4946-e6cd-9e99d4e53eb7"
      },
      "source": [
        "25*0 + 2*1 + 5*2"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "12"
            ]
          },
          "metadata": {},
          "execution_count": 9
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "ThehRrr8cgvS",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "4c29c389-a160-4f1d-f5a1-377a4b3d7a8b"
      },
      "source": [
        "np.dot(x, y)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "12"
            ]
          },
          "metadata": {},
          "execution_count": 10
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "J5Zdua4xcgvT",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "e2b09f45-b7e1-4cec-dca6-fc16ae58e262"
      },
      "source": [
        "x_pt"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "tensor([25,  2,  5])"
            ]
          },
          "metadata": {},
          "execution_count": 11
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "b3vEdroXcgvU",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "b5c93798-c29a-43c5-a66b-779c05c28f10"
      },
      "source": [
        "y_pt = torch.tensor([0, 1, 2])\n",
        "y_pt"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "tensor([0, 1, 2])"
            ]
          },
          "metadata": {},
          "execution_count": 12
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "F741E5imcgvV",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "5b1f2dc2-6c1f-4e54-b31a-fb05b503bf76"
      },
      "source": [
        "np.dot(x_pt, y_pt)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "12"
            ]
          },
          "metadata": {},
          "execution_count": 13
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "-W5loHc8cgvX",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "8d3372f7-ebf2-4b30-ed17-9ee8b586f22a"
      },
      "source": [
        "torch.dot(torch.tensor([25, 2, 5.]), torch.tensor([0, 1, 2.]))"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "tensor(12.)"
            ]
          },
          "metadata": {},
          "execution_count": 16
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "jUwKBiqzcgvY",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "780960ca-39e6-499c-995c-f27e8c2a9a9b"
      },
      "source": [
        "x_tf"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<tf.Variable 'Variable:0' shape=(3,) dtype=int32, numpy=array([25,  2,  5], dtype=int32)>"
            ]
          },
          "metadata": {},
          "execution_count": 17
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "Xqt3Rac7cgvZ",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "e1b8618a-81f3-46f2-cf8f-85d65302828f"
      },
      "source": [
        "y_tf = tf.Variable([0, 1, 2])\n",
        "y_tf"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<tf.Variable 'Variable:0' shape=(3,) dtype=int32, numpy=array([0, 1, 2], dtype=int32)>"
            ]
          },
          "metadata": {},
          "execution_count": 18
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "x4pgc5JEcgvc",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "96631b91-b352-4844-82a2-6a28eb868a8c"
      },
      "source": [
        "tf.reduce_sum(tf.multiply(x_tf, y_tf))"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<tf.Tensor: shape=(), dtype=int32, numpy=12>"
            ]
          },
          "metadata": {},
          "execution_count": 19
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "mSmvC1cc6SMj"
      },
      "source": [
        "**Volver a las slides aquí.**"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "9dfTV7hQR6zn"
      },
      "source": [
        "### Resolución de Sistemas Lineales"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "pCoSpqtWSyFd"
      },
      "source": [
        "En el ejemplo de **Sustitución**, las dos ecuaciones del sistema son:\n",
        "$$ y = 3x $$\n",
        "$$ -5x + 2y = 2 $$\n",
        "\n",
        "La segunda ecuación puede reordenarse para aislar $y$:\n",
        "$$ 2y = 2 + 5x $$\n",
        "$$ y = \\frac{2 + 5x}{2} = 1 + \\frac{5x}{2} $$"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "1T0_m11kTh82"
      },
      "source": [
        "x = np.linspace(-10, 10, 1000) # inicio, final, n puntos"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "_K6IyUWcTh85"
      },
      "source": [
        "y1 = 3 * x"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "DYkQdUJ5Th86"
      },
      "source": [
        "y2 = 1 + (5*x)/2"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 476
        },
        "id": "aBL9NDoHTh86",
        "outputId": "c6746aaa-1352-4290-d1b4-e9006f85f281"
      },
      "source": [
        "fig, ax = plt.subplots()\n",
        "plt.xlabel('x')\n",
        "plt.ylabel('y')\n",
        "ax.set_xlim([0, 3])\n",
        "ax.set_ylim([0, 8])\n",
        "ax.plot(x, y1, c='green')\n",
        "ax.plot(x, y2, c='brown')\n",
        "plt.axvline(x=2, color='purple', linestyle='--')\n",
        "_ = plt.axhline(y=6, color='purple', linestyle='--')"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "**Volver a las slides aquí.**"
      ],
      "metadata": {
        "id": "vACSnJgP87xA"
      }
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "F3X4p66XVFXH"
      },
      "source": [
        "En el ejemplo de **Eliminación**, las dos ecuaciones del sistema son:\n",
        "$$ 2x - 3y = 15 $$\n",
        "$$ 4x + 10y = 14 $$\n",
        "\n",
        "Ambas ecuaciones pueden reordenarse para aislar $y$. A partir de la primera ecuación:\n",
        "$$ -3y = 15 - 2x $$\n",
        "$$ y = \\frac{15 - 2x}{-3} = -5 + \\frac{2x}{3} $$\n",
        "\n",
        "Si operamos con la segunda ecuación:\n",
        "$$ 4x + 10y = 14 $$\n",
        "$$ 2x + 5y = 7 $$\n",
        "$$ 5y = 7 - 2x $$\n",
        "$$ y = \\frac{7 - 2x}{5} $$"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "5x3kfV_WWhlR"
      },
      "source": [
        "y1 = -5 + (2*x)/3"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "dqA1lS0CWu5z"
      },
      "source": [
        "y2 = (7-2*x)/5"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "6CfRNs1DWzx5",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 476
        },
        "outputId": "677bdaf1-1490-43dc-9c39-5ede6d8d7faf"
      },
      "source": [
        "fig, ax = plt.subplots()\n",
        "plt.xlabel('x')\n",
        "plt.ylabel('y')\n",
        "\n",
        "# Añadimos los ejes x e y:\n",
        "plt.axvline(x=0, color='lightgray')\n",
        "plt.axhline(y=0, color='lightgray')\n",
        "\n",
        "ax.set_xlim([-2, 10])\n",
        "ax.set_ylim([-6, 4])\n",
        "ax.plot(x, y1, c='green')\n",
        "ax.plot(x, y2, c='brown')\n",
        "plt.axvline(x=6, color='purple', linestyle='--')\n",
        "_ = plt.axhline(y=-1, color='purple', linestyle='--')"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "**Volver a las slides aquí.**"
      ],
      "metadata": {
        "id": "CezB87Tb-QGh"
      }
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "bYDhomCP6SMj"
      },
      "source": [
        "## Segmento 3: Propiedades de las Matrices"
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "import numpy as np\n",
        "import torch\n",
        "import tensorflow as tf"
      ],
      "metadata": {
        "id": "gCBOE7sUH_Au"
      },
      "execution_count": 2,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "-HGU_an66SMk"
      },
      "source": [
        "### La Norma de Frobenius"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "pNQHvAqN6SMk",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "13933b24-2771-4237-8626-972d1254c31b"
      },
      "source": [
        "X = np.array([[1, 2], [3, 4]])\n",
        "X"
      ],
      "execution_count": 4,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[1, 2],\n",
              "       [3, 4]])"
            ]
          },
          "metadata": {},
          "execution_count": 4
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "T-q-Tzn26SMm",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "93d2b861-c86d-458a-fc17-64bb566e2128"
      },
      "source": [
        "(1**2 + 2**2 + 3**2 + 4**2)**(1/2)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "5.477225575051661"
            ]
          },
          "metadata": {},
          "execution_count": 3
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "YVG8qiFw6SMn",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "c7c9d978-5985-4138-f3d1-7e1a61b79cb4"
      },
      "source": [
        "np.linalg.norm(X) # la misma función que para la norma vectorial L2"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "5.477225575051661"
            ]
          },
          "metadata": {},
          "execution_count": 4
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "FPnBflKVxyik"
      },
      "source": [
        "X_pt = torch.tensor([[1, 2], [3, 4.]]) # torch.norm() solamente soporta floats"
      ],
      "execution_count": 5,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "NCdTShVyx8z0",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "8a60e51f-fdfa-4ae3-9acf-a9480331419d"
      },
      "source": [
        "torch.norm(X_pt)"
      ],
      "execution_count": 6,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "tensor(5.4772)"
            ]
          },
          "metadata": {},
          "execution_count": 6
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "blezf9fLx_nD"
      },
      "source": [
        "X_tf = tf.Variable([[1, 2], [3, 4.]]) # tf.norm() solamente soporta floats"
      ],
      "execution_count": 7,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "LiCQzyf6ySCZ",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "1a5468f3-c71f-46b4-e70c-d3f2bc248893"
      },
      "source": [
        "tf.norm(X_tf)"
      ],
      "execution_count": 8,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<tf.Tensor: shape=(), dtype=float32, numpy=5.477226>"
            ]
          },
          "metadata": {},
          "execution_count": 8
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "4c6rjVAf6SMo"
      },
      "source": [
        "**Volver a las slides aquí.**"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "OLN-MMIe6SMo"
      },
      "source": [
        "### Multiplicación de Matrices (por un Vector)"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "XJw0j8cr6SMo",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "ca09a355-32bf-4d1c-826e-b3ebdeba20c1"
      },
      "source": [
        "A = np.array([[3, 4], [5, 6], [7, 8]])\n",
        "A"
      ],
      "execution_count": 9,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[3, 4],\n",
              "       [5, 6],\n",
              "       [7, 8]])"
            ]
          },
          "metadata": {},
          "execution_count": 9
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "zZQ1Aupc6SMq",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "8d577b6a-3a5d-45d7-e442-b382f8baca09"
      },
      "source": [
        "b = np.array([1, 2])\n",
        "b"
      ],
      "execution_count": 10,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([1, 2])"
            ]
          },
          "metadata": {},
          "execution_count": 10
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "ZbeVtNyW6SMq",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "d13dcb35-de9b-4819-fdfc-455a35e97f33"
      },
      "source": [
        "np.dot(A, b) # aunque técnicamente el producto punto es sólo entre vectores"
      ],
      "execution_count": 11,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([11, 17, 23])"
            ]
          },
          "metadata": {},
          "execution_count": 11
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "srVI55X96SMu",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "cefe93de-a052-4066-99e1-1bb363b36c10"
      },
      "source": [
        "A_pt = torch.tensor([[3, 4], [5, 6], [7, 8]])\n",
        "A_pt"
      ],
      "execution_count": 12,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "tensor([[3, 4],\n",
              "        [5, 6],\n",
              "        [7, 8]])"
            ]
          },
          "metadata": {},
          "execution_count": 12
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "5SDn71Xc6SMv",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "9a7b3ab7-544c-49bc-83eb-33195880d10a"
      },
      "source": [
        "b_pt = torch.tensor([1, 2])\n",
        "b_pt"
      ],
      "execution_count": 13,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "tensor([1, 2])"
            ]
          },
          "metadata": {},
          "execution_count": 13
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "OIeoJlsh6SMx",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "fb040e47-92a3-46b1-d81f-3d80f7acece3"
      },
      "source": [
        "torch.matmul(A_pt, b_pt) # como np.dot(), infiere automáticamente las dimensiones para realizar producto punto, matvec, o multiplicación de matrices."
      ],
      "execution_count": 14,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "tensor([11, 17, 23])"
            ]
          },
          "metadata": {},
          "execution_count": 14
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "pnob9GkB6SMs",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "8eb37779-6254-4c0a-9423-9b145a24588c"
      },
      "source": [
        "A_tf = tf.Variable([[3, 4], [5, 6], [7, 8]])\n",
        "A_tf"
      ],
      "execution_count": 15,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<tf.Variable 'Variable:0' shape=(3, 2) dtype=int32, numpy=\n",
              "array([[3, 4],\n",
              "       [5, 6],\n",
              "       [7, 8]], dtype=int32)>"
            ]
          },
          "metadata": {},
          "execution_count": 15
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "vYtWxf8K6SMt",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "6d7606ca-2429-4db6-c29c-09de3c76e24a"
      },
      "source": [
        "b_tf = tf.Variable([1, 2])\n",
        "b_tf"
      ],
      "execution_count": 16,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<tf.Variable 'Variable:0' shape=(2,) dtype=int32, numpy=array([1, 2], dtype=int32)>"
            ]
          },
          "metadata": {},
          "execution_count": 16
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "NGBImWRH6SMt",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "4929cb18-90f4-4b47-cab1-883e59845579"
      },
      "source": [
        "tf.linalg.matvec(A_tf, b_tf)"
      ],
      "execution_count": 17,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<tf.Tensor: shape=(3,), dtype=int32, numpy=array([11, 17, 23], dtype=int32)>"
            ]
          },
          "metadata": {},
          "execution_count": 17
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "kzjZmdRR6SMy"
      },
      "source": [
        "**Volver a las slides aquí.**"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "21ySqay36SM5"
      },
      "source": [
        "### Multiplicación de Matrices (con Dos Matrices)"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "0YRG1Ig2cgvo",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "f01fe337-cf96-41a1-ccbb-7cd51a687b30"
      },
      "source": [
        "A"
      ],
      "execution_count": 18,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[3, 4],\n",
              "       [5, 6],\n",
              "       [7, 8]])"
            ]
          },
          "metadata": {},
          "execution_count": 18
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "DyOEZk_c6SM5",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "a9f45988-e999-4115-b0fc-2fe3c73c59b6"
      },
      "source": [
        "B = np.array([[1, 9], [2, 0]])\n",
        "B"
      ],
      "execution_count": 19,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[1, 9],\n",
              "       [2, 0]])"
            ]
          },
          "metadata": {},
          "execution_count": 19
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "SfKuNxH-6SM6",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "e270b0a5-b445-4c17-821a-606b04cd77d0"
      },
      "source": [
        "np.dot(A, B)"
      ],
      "execution_count": 20,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[11, 27],\n",
              "       [17, 45],\n",
              "       [23, 63]])"
            ]
          },
          "metadata": {},
          "execution_count": 20
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "WcnQMF0s6SNB"
      },
      "source": [
        "Tenga en cuenta que la multiplicación de matrices no es \"conmutativa\" (es decir, $AB \\neq BA$) por lo que al descomentar la línea siguiente se producirá un error de desajuste de tamaño:"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "_mwBGOXO6SNB"
      },
      "source": [
        "# np.dot(B, A)"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "JrrvPoNE6SM9",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "1e07e3f2-4079-4707-a6b1-0e3ebf7a05e6"
      },
      "source": [
        "B_pt = torch.from_numpy(B) # más limpia que la conversión de TF\n",
        "B_pt"
      ],
      "execution_count": 21,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "tensor([[1, 9],\n",
              "        [2, 0]])"
            ]
          },
          "metadata": {},
          "execution_count": 21
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "Z6PfwCvX6SM-",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "5dfc196c-9aa8-48d4-bb4c-7a877763e340"
      },
      "source": [
        "# otra forma de crear el mismo tensor con transposición:\n",
        "B_pt = torch.tensor([[1, 2], [9, 0]]).T\n",
        "B_pt"
      ],
      "execution_count": 22,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "tensor([[1, 9],\n",
              "        [2, 0]])"
            ]
          },
          "metadata": {},
          "execution_count": 22
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "16ZNRaVe6SM_",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "7c5eb0c5-8b6c-485b-b81d-a6e238d0f887"
      },
      "source": [
        "torch.matmul(A_pt, B_pt) # no se necesita cambiar la función, a diferencia de TF"
      ],
      "execution_count": 23,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "tensor([[11, 27],\n",
              "        [17, 45],\n",
              "        [23, 63]])"
            ]
          },
          "metadata": {},
          "execution_count": 23
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "rkymNjE46SM8",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "eb75d25d-91cd-4507-9584-59a2b061ed1e"
      },
      "source": [
        "B_tf = tf.convert_to_tensor(B, dtype=tf.int32)\n",
        "B_tf"
      ],
      "execution_count": 24,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<tf.Tensor: shape=(2, 2), dtype=int32, numpy=\n",
              "array([[1, 9],\n",
              "       [2, 0]], dtype=int32)>"
            ]
          },
          "metadata": {},
          "execution_count": 24
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "rslTzFRk6SM8",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "5970ddb5-e35f-4b70-c0e9-ddcfc5f9cdc6"
      },
      "source": [
        "tf.matmul(A_tf, B_tf)"
      ],
      "execution_count": 25,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<tf.Tensor: shape=(3, 2), dtype=int32, numpy=\n",
              "array([[11, 27],\n",
              "       [17, 45],\n",
              "       [23, 63]], dtype=int32)>"
            ]
          },
          "metadata": {},
          "execution_count": 25
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "0eBiTmPp6SNC"
      },
      "source": [
        "**Volver a las slides aquí.**"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "L2H9F-DQ6SMz"
      },
      "source": [
        "### Matrices Simétricas"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "5YsPoWo76SMz",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "bbf91f6c-c6e5-4ecf-ea02-c38dc31fbb97"
      },
      "source": [
        "X_sym = np.array([[0, 1, 2], [1, 7, 8], [2, 8, 9]])\n",
        "X_sym"
      ],
      "execution_count": 27,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[0, 1, 2],\n",
              "       [1, 7, 8],\n",
              "       [2, 8, 9]])"
            ]
          },
          "metadata": {},
          "execution_count": 27
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "Skg1wSQVcgv2",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "312b7973-c581-4817-c415-48493149bad8"
      },
      "source": [
        "X_sym.T"
      ],
      "execution_count": 28,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[0, 1, 2],\n",
              "       [1, 7, 8],\n",
              "       [2, 8, 9]])"
            ]
          },
          "metadata": {},
          "execution_count": 28
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "Jv40-i9H6SM1",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "c2a79105-3e3d-4a59-d0e1-02c610af0cf6"
      },
      "source": [
        "X_sym.T == X_sym"
      ],
      "execution_count": 29,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[ True,  True,  True],\n",
              "       [ True,  True,  True],\n",
              "       [ True,  True,  True]])"
            ]
          },
          "metadata": {},
          "execution_count": 29
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "QZFoUFkq6SM2"
      },
      "source": [
        "**Volver a las slides aquí.**"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Mq_c3ftZ6SM2"
      },
      "source": [
        "### Matrices Identidad"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "KVSNbH-Z6SM2",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "3164258a-eda1-4f35-c44d-bca5527e7f03"
      },
      "source": [
        "I = torch.tensor([[1, 0, 0], [0, 1, 0], [0, 0, 1]])\n",
        "I"
      ],
      "execution_count": 30,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "tensor([[1, 0, 0],\n",
              "        [0, 1, 0],\n",
              "        [0, 0, 1]])"
            ]
          },
          "metadata": {},
          "execution_count": 30
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "wcoPDhvR6SM3",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "0a58d462-1892-488b-bc9e-b976149f609c"
      },
      "source": [
        "x_pt = torch.tensor([25, 2, 5])\n",
        "x_pt"
      ],
      "execution_count": 31,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "tensor([25,  2,  5])"
            ]
          },
          "metadata": {},
          "execution_count": 31
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "tuA4RsMv6SM4",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "f0577e6e-0c15-4e9d-acb0-02e5d2eed137"
      },
      "source": [
        "torch.matmul(I, x_pt)"
      ],
      "execution_count": 32,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "tensor([25,  2,  5])"
            ]
          },
          "metadata": {},
          "execution_count": 32
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "bgDiOYLk6SM5"
      },
      "source": [
        "**Volver a las slides aquí.**"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "3S_6Yfdkcgv7"
      },
      "source": [
        "### Respuestas a las preguntas sobre multiplicación de matrices"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "pINsKNxH6SNC",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "8dc871c8-6ab3-4cfa-f03a-657422945035"
      },
      "source": [
        "M_q = torch.tensor([[0, 1, 2], [3, 4, 5], [6, 7, 8]])\n",
        "M_q"
      ],
      "execution_count": 33,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "tensor([[0, 1, 2],\n",
              "        [3, 4, 5],\n",
              "        [6, 7, 8]])"
            ]
          },
          "metadata": {},
          "execution_count": 33
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "gfjWd8OO6SNE",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "6916024e-730f-4572-de87-0b5bed0b160f"
      },
      "source": [
        "V_q = torch.tensor([[-1, 1, -2], [0, 1, 2]]).T\n",
        "V_q"
      ],
      "execution_count": 34,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "tensor([[-1,  0],\n",
              "        [ 1,  1],\n",
              "        [-2,  2]])"
            ]
          },
          "metadata": {},
          "execution_count": 34
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "boSkaV2M6SNF",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "1018737b-e97e-4f0f-e8fe-143283562532"
      },
      "source": [
        "torch.matmul(M_q, V_q)"
      ],
      "execution_count": 35,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "tensor([[ -3,   5],\n",
              "        [ -9,  14],\n",
              "        [-15,  23]])"
            ]
          },
          "metadata": {},
          "execution_count": 35
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "slSNKUcN6SNG"
      },
      "source": [
        "### Inversión de Matrices"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "EW0i5ZRk6SNG",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "80549371-94d2-40e3-b4d5-cb80cddff397"
      },
      "source": [
        "X = np.array([[4, 2], [-5, -3]])\n",
        "X"
      ],
      "execution_count": 36,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[ 4,  2],\n",
              "       [-5, -3]])"
            ]
          },
          "metadata": {},
          "execution_count": 36
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "hTYpxaWR6SNI",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "b9c642ec-50c3-45ca-bea8-10d358d47cd5"
      },
      "source": [
        "Xinv = np.linalg.inv(X)\n",
        "Xinv"
      ],
      "execution_count": 37,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[ 1.5,  1. ],\n",
              "       [-2.5, -2. ]])"
            ]
          },
          "metadata": {},
          "execution_count": 37
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "XFDBBdYOc-7E"
      },
      "source": [
        "Como un rápido aporte, vamos a demostrar que $X^{-1}X = I_n$ según las diapositivas:"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "tyPhf-uZcvdB",
        "outputId": "b476d6ec-b1e1-4407-8d92-1edbc6e18245",
        "colab": {
          "base_uri": "https://localhost:8080/"
        }
      },
      "source": [
        "np.round(np.dot(Xinv, X))"
      ],
      "execution_count": 39,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[1., 0.],\n",
              "       [0., 1.]])"
            ]
          },
          "metadata": {},
          "execution_count": 39
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "SVwvbBvclul1"
      },
      "source": [
        "...y ahora volvemos a resolver las incógnitas en $w$:"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "Q5sQqFaz6SNK",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "8b326427-aef8-4a2c-f030-942df5bf37b1"
      },
      "source": [
        "y = np.array([4, -7])\n",
        "y"
      ],
      "execution_count": 40,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([ 4, -7])"
            ]
          },
          "metadata": {},
          "execution_count": 40
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "PK7m6F1I6SNL",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "fe84f9d4-3b7b-4c93-c769-b0e3489daa8f"
      },
      "source": [
        "w = np.dot(Xinv, y)\n",
        "w"
      ],
      "execution_count": 41,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([-1.,  4.])"
            ]
          },
          "metadata": {},
          "execution_count": 41
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "fyBOHgdccgwD"
      },
      "source": [
        "De modo que $y = Xw$:"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "SVBojjwacgwD",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "ad2dd165-c3fd-4ab5-c794-f488291a2b40"
      },
      "source": [
        "np.dot(X, w)"
      ],
      "execution_count": 42,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([ 4., -7.])"
            ]
          },
          "metadata": {},
          "execution_count": 42
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "rKELsi0PZCr0"
      },
      "source": [
        "**Visualización Geométrica**\n",
        "\n",
        "Recordando de las diapositivas que las dos ecuaciones del sistema son:\n",
        "$$ 4b + 2c = 4 $$\n",
        "$$ -5b - 3c = -7 $$\n",
        "\n",
        "Ambas ecuaciones pueden reordenarse para aislar una variable, digamos $c$. A partir de la primera ecuación:\n",
        "$$ 4b + 2c = 4 $$\n",
        "$$ 2b + c = 2 $$\n",
        "$$ c = 2 - 2b $$\n",
        "\n",
        "Entonces para la segunda ecuación:\n",
        "$$ -5b - 3c = -7 $$\n",
        "$$ -3c = -7 + 5b $$\n",
        "$$ c = \\frac{-7 + 5b}{-3} = \\frac{7 - 5b}{3} $$"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "ZASIBqroap7k"
      },
      "source": [
        "b = np.linspace(-10, 10, 1000) # inicio, final, n puntos"
      ],
      "execution_count": 43,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "9XsUdVsmaqTr"
      },
      "source": [
        "c1 = 2 - 2*b"
      ],
      "execution_count": 44,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "8Mwn1tAca1Cl"
      },
      "source": [
        "c2 = (7-5*b)/3"
      ],
      "execution_count": 45,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "import matplotlib.pyplot as plt"
      ],
      "metadata": {
        "id": "To1agkv3qUOQ"
      },
      "execution_count": 47,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "X5ozP9jZauQa",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 476
        },
        "outputId": "7b8e334d-394c-4461-a17b-92e0cf2b3f0b"
      },
      "source": [
        "fig, ax = plt.subplots()\n",
        "plt.xlabel('b', c='darkorange')\n",
        "plt.ylabel('c', c='brown')\n",
        "\n",
        "plt.axvline(x=0, color='lightgray')\n",
        "plt.axhline(y=0, color='lightgray')\n",
        "\n",
        "ax.set_xlim([-2, 3])\n",
        "ax.set_ylim([-1, 5])\n",
        "ax.plot(b, c1, c='purple')\n",
        "ax.plot(b, c2, c='purple')\n",
        "plt.axvline(x=-1, color='green', linestyle='--')\n",
        "_ = plt.axhline(y=4, color='green', linestyle='--')"
      ],
      "execution_count": 48,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "14uhePTna7ZV"
      },
      "source": [
        "En PyTorch y TensorFlow:"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "7qo-SAvaansp",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "31d9061c-767c-4488-8ec5-e9f2507a01da"
      },
      "source": [
        "torch.inverse(torch.tensor([[4, 2], [-5, -3.]])) # tipo float"
      ],
      "execution_count": 49,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "tensor([[ 1.5000,  1.0000],\n",
              "        [-2.5000, -2.0000]])"
            ]
          },
          "metadata": {},
          "execution_count": 49
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "uqtyF3Jqaz4l",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "4c7259d3-4113-4700-e597-525007aa25e6"
      },
      "source": [
        "tf.linalg.inv(tf.Variable([[4, 2], [-5, -3.]])) # también float"
      ],
      "execution_count": 50,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<tf.Tensor: shape=(2, 2), dtype=float32, numpy=\n",
              "array([[ 1.4999998,  0.9999998],\n",
              "       [-2.4999995, -1.9999996]], dtype=float32)>"
            ]
          },
          "metadata": {},
          "execution_count": 50
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "hcP2S4AMAHT_"
      },
      "source": [
        "**Ejercicios**:\n",
        "\n",
        "1. Como se hizo anteriormente con NumPy, utilizar PyTorch para calcular $w$ a partir de $X$ e $y$. Posteriormente, confirmar que $y = Xw$.\n",
        "2. Repetir de nuevo, ahora utilizando TensorFlow."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "AMxROg326SNN"
      },
      "source": [
        "**Volver a las slides aquí.**"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "N8ZxpgcN6SNO"
      },
      "source": [
        "### Inversión de la matriz cuando no hay solución"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "RYORHY4E6SNO",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "71f916b8-15c1-4507-dc33-bd1870eb70f4"
      },
      "source": [
        "X = np.array([[-4, 1], [-8, 2]])\n",
        "X"
      ],
      "execution_count": 51,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[-4,  1],\n",
              "       [-8,  2]])"
            ]
          },
          "metadata": {},
          "execution_count": 51
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "o7GcISdI6SNP",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 313
        },
        "outputId": "fbbfe47f-6dda-453d-dfbd-ec0d696f512e"
      },
      "source": [
        "# Descomentar la línea siguiente da lugar a un error de \"matriz singular\n",
        "# Xinv = np.linalg.inv(X)"
      ],
      "execution_count": 52,
      "outputs": [
        {
          "output_type": "error",
          "ename": "LinAlgError",
          "evalue": "Singular matrix",
          "traceback": [
            "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
            "\u001b[0;31mLinAlgError\u001b[0m                               Traceback (most recent call last)",
            "\u001b[0;32m<ipython-input-52-5092751262ca>\u001b[0m in \u001b[0;36m<cell line: 2>\u001b[0;34m()\u001b[0m\n\u001b[1;32m      1\u001b[0m \u001b[0;31m# Descomentar la línea siguiente da lugar a un error de \"matriz singular\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m----> 2\u001b[0;31m \u001b[0mXinv\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mnp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mlinalg\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0minv\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mX\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m",
            "\u001b[0;32m/usr/local/lib/python3.10/dist-packages/numpy/linalg/linalg.py\u001b[0m in \u001b[0;36minv\u001b[0;34m(a)\u001b[0m\n\u001b[1;32m    559\u001b[0m     \u001b[0msignature\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;34m'D->D'\u001b[0m \u001b[0;32mif\u001b[0m \u001b[0misComplexType\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mt\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;32melse\u001b[0m \u001b[0;34m'd->d'\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    560\u001b[0m     \u001b[0mextobj\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mget_linalg_error_extobj\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0m_raise_linalgerror_singular\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 561\u001b[0;31m     \u001b[0mainv\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0m_umath_linalg\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0minv\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0ma\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0msignature\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0msignature\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mextobj\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mextobj\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    562\u001b[0m     \u001b[0;32mreturn\u001b[0m \u001b[0mwrap\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mainv\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mastype\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mresult_t\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mcopy\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;32mFalse\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    563\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n",
            "\u001b[0;32m/usr/local/lib/python3.10/dist-packages/numpy/linalg/linalg.py\u001b[0m in \u001b[0;36m_raise_linalgerror_singular\u001b[0;34m(err, flag)\u001b[0m\n\u001b[1;32m    110\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    111\u001b[0m \u001b[0;32mdef\u001b[0m \u001b[0m_raise_linalgerror_singular\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0merr\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mflag\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 112\u001b[0;31m     \u001b[0;32mraise\u001b[0m \u001b[0mLinAlgError\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m\"Singular matrix\"\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    113\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    114\u001b[0m \u001b[0;32mdef\u001b[0m \u001b[0m_raise_linalgerror_nonposdef\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0merr\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mflag\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
            "\u001b[0;31mLinAlgError\u001b[0m: Singular matrix"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "uk485dwoI021"
      },
      "source": [
        "Siéntase libre de intentar invertir una matriz no cuadrada; esto también arrojará un error.\n",
        "\n",
        "**Vuelve a las slides aquí.**"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "BXomEBoyDQyO"
      },
      "source": [
        "### Matrices Ortogonales\n",
        "\n",
        "Estas son las soluciones a los Ejercicios 3 y 4 sobre **matrices ortogonales** de las diapositivas.\n",
        "\n",
        "En el Ejercicio 3, para demostrar que la matriz $I_3$ tiene columnas mutuamente ortogonales, demostramos que el producto escalar de cualquier par de columnas es cero:"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "-Un4Aq805HM1",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "12f8f7dc-502c-4b62-de35-0f9feab17995"
      },
      "source": [
        "I = np.array([[1, 0, 0], [0, 1, 0], [0, 0, 1]])\n",
        "I"
      ],
      "execution_count": 54,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[1, 0, 0],\n",
              "       [0, 1, 0],\n",
              "       [0, 0, 1]])"
            ]
          },
          "metadata": {},
          "execution_count": 54
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "CUhMi2_IEyaI",
        "outputId": "6a1c3ad6-a940-4645-f428-03353a55f5aa"
      },
      "source": [
        "column_1 = I[:,0]\n",
        "column_1"
      ],
      "execution_count": 55,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([1, 0, 0])"
            ]
          },
          "metadata": {},
          "execution_count": 55
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "xsOtn-siE63K",
        "outputId": "fbb90fc4-0668-4694-82ab-00de919eb9f9"
      },
      "source": [
        "column_2 = I[:,1]\n",
        "column_2"
      ],
      "execution_count": 56,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([0, 1, 0])"
            ]
          },
          "metadata": {},
          "execution_count": 56
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "Pv3b51ExE9ZX",
        "outputId": "4f57705c-299c-4521-f099-62e1feb32365"
      },
      "source": [
        "column_3 = I[:,2]\n",
        "column_3"
      ],
      "execution_count": 57,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([0, 0, 1])"
            ]
          },
          "metadata": {},
          "execution_count": 57
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "VhnRlc8eElYc",
        "outputId": "b096fe90-4712-4394-c35e-894bb62e51f0"
      },
      "source": [
        "np.dot(column_1, column_2)"
      ],
      "execution_count": 58,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "0"
            ]
          },
          "metadata": {},
          "execution_count": 58
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "mVq4m-LfFGjQ",
        "outputId": "2f671521-a048-4d2d-9a8d-51216fba9311"
      },
      "source": [
        "np.dot(column_1, column_3)"
      ],
      "execution_count": 59,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "0"
            ]
          },
          "metadata": {},
          "execution_count": 59
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "nJj-aihzFILx",
        "outputId": "d14273ac-5632-4682-b0d3-0facd0163d96"
      },
      "source": [
        "np.dot(column_2, column_3)"
      ],
      "execution_count": 60,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "0"
            ]
          },
          "metadata": {},
          "execution_count": 60
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "FIzpkdJmFYdY"
      },
      "source": [
        "Podemos utilizar el método `np.linalg.norm()` de antes en el cuaderno para demostrar que cada columna de $I_3$ tiene norma unitaria:"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "xKbbeqegFJSc",
        "outputId": "55e02114-c271-46c3-fd57-42495397e452"
      },
      "source": [
        "np.linalg.norm(column_1)"
      ],
      "execution_count": 61,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "1.0"
            ]
          },
          "metadata": {},
          "execution_count": 61
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "Ycv0L8mpGKRC",
        "outputId": "25a3a4f6-9b8c-4fa6-89cc-83d7ff9ba856"
      },
      "source": [
        "np.linalg.norm(column_2)"
      ],
      "execution_count": 62,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "1.0"
            ]
          },
          "metadata": {},
          "execution_count": 62
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "LsEuRezYGLgY",
        "outputId": "07ba6f7f-1c29-46cb-a0a8-bc4c1274fdd2"
      },
      "source": [
        "np.linalg.norm(column_3)"
      ],
      "execution_count": 63,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "1.0"
            ]
          },
          "metadata": {},
          "execution_count": 63
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "NMrHdyrsGQ1X"
      },
      "source": [
        "Como la matriz $I_3$ tiene columnas mutuamente ortogonales y cada columna tiene norma unitaria, los vectores columna de $I_3$ son *ortonormales*. Dado que $I_3^T = I_3$, esto significa que las *filas* de $I_3$ también deben ser ortonormales.\n",
        "\n",
        "Puesto que las columnas y las filas de $I_3$ son ortonormales, $I_3$ es una *matriz ortogonal*."
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "K7EykcPdIZhE"
      },
      "source": [
        "Para el Ejercicio 4, vamos a repetir los pasos del Ejercicio 3 con la matriz *K* en lugar de $I_3$. Podríamos usar NumPy de nuevo, pero por diversión usaré PyTorch en su lugar. (¡Eres bienvenido a intentarlo con TensorFlow si te sientes con ganas!)."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "MXVyu8tSGMlZ",
        "outputId": "69956bf6-5981-4165-99b8-6893c719563a"
      },
      "source": [
        "K = torch.tensor([[2/3, 1/3, 2/3], [-2/3, 2/3, 1/3], [1/3, 2/3, -2/3]])\n",
        "K"
      ],
      "execution_count": 64,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "tensor([[ 0.6667,  0.3333,  0.6667],\n",
              "        [-0.6667,  0.6667,  0.3333],\n",
              "        [ 0.3333,  0.6667, -0.6667]])"
            ]
          },
          "metadata": {},
          "execution_count": 64
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "xqkmSYNfJmTs",
        "outputId": "e0eefe08-e2e3-4b24-912b-0a330fc21ac2"
      },
      "source": [
        "Kcol_1 = K[:,0]\n",
        "Kcol_1"
      ],
      "execution_count": 65,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "tensor([ 0.6667, -0.6667,  0.3333])"
            ]
          },
          "metadata": {},
          "execution_count": 65
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "ncoc3IxNJ0v2",
        "outputId": "6f4ec37d-573b-405e-f337-7552952fde77"
      },
      "source": [
        "Kcol_2 = K[:,1]\n",
        "Kcol_2"
      ],
      "execution_count": 66,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "tensor([0.3333, 0.6667, 0.6667])"
            ]
          },
          "metadata": {},
          "execution_count": 66
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "ISEKQ0AqJ2wf",
        "outputId": "53504be6-fc21-429c-d71d-0bd9ec30ae07"
      },
      "source": [
        "Kcol_3 = K[:,2]\n",
        "Kcol_3"
      ],
      "execution_count": 67,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "tensor([ 0.6667,  0.3333, -0.6667])"
            ]
          },
          "metadata": {},
          "execution_count": 67
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "jvdXuMzbJ44d",
        "outputId": "ab989ef4-df3f-495b-c9d8-360bedf835e7"
      },
      "source": [
        "torch.dot(Kcol_1, Kcol_2)"
      ],
      "execution_count": 68,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "tensor(0.)"
            ]
          },
          "metadata": {},
          "execution_count": 68
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "BUR60eBuKEbU",
        "outputId": "c0ed33b1-2005-4276-969e-2d586215b2d0"
      },
      "source": [
        "torch.dot(Kcol_1, Kcol_3)"
      ],
      "execution_count": 69,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "tensor(0.)"
            ]
          },
          "metadata": {},
          "execution_count": 69
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "Rg7QvQwuKGJZ",
        "outputId": "19245bb2-56a7-4bcd-9d28-18c9c968dec7"
      },
      "source": [
        "torch.dot(Kcol_2, Kcol_3)"
      ],
      "execution_count": 70,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "tensor(0.)"
            ]
          },
          "metadata": {},
          "execution_count": 70
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "wNdV36-QKNK-"
      },
      "source": [
        "Ahora hemos determinado que las columnas de $K$ son ortogonales."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "DDgyhj1AKHdS",
        "outputId": "018dc13d-9b98-4d91-87bb-1edb2a5561bc"
      },
      "source": [
        "torch.norm(Kcol_1)"
      ],
      "execution_count": 71,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "tensor(1.)"
            ]
          },
          "metadata": {},
          "execution_count": 71
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "KvQZy_E2KorW",
        "outputId": "cf914f2e-ab21-4103-ca90-6b73d0cbc7fd"
      },
      "source": [
        "torch.norm(Kcol_2)"
      ],
      "execution_count": 72,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "tensor(1.)"
            ]
          },
          "metadata": {},
          "execution_count": 72
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "7H7dx8a7Kp9f",
        "outputId": "0228d1f1-85a8-4966-cb36-e96db8e5ae8c"
      },
      "source": [
        "torch.norm(Kcol_3)"
      ],
      "execution_count": 73,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "tensor(1.)"
            ]
          },
          "metadata": {},
          "execution_count": 73
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "VPPtOk5OKtJ_"
      },
      "source": [
        "Ahora hemos determinado que, además de ser ortogonales, las columnas de $K$ tienen norma unitaria, por lo tanto son ortonormales.\n",
        "\n",
        "Para asegurar que $K$ es una matriz ortogonal, tendríamos que demostrar que no sólo tiene columnas ortonormales sino que también tiene filas ortonormales. Desde $ K^T \\neq K $, no podemos demostrar esto tan directamente como lo hicimos con $ I_3 $.\n",
        "\n",
        "Un enfoque sería repetir los pasos que utilizamos para determinar que $K$ tiene columnas ortogonales con todas las filas de la matriz (por favor, siéntase libre de hacerlo). Alternativamente, podemos utilizar una ecuación específica de matriz ortogonal de las diapositivas, $A^TA = I$, para demostrar que $K$ es ortogonal en una sola línea de código:"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "W8Ao0KhVNHqF",
        "outputId": "5a20de45-9271-4444-801b-f839e1dbdd32"
      },
      "source": [
        "torch.matmul(K.T, K)"
      ],
      "execution_count": 74,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "tensor([[ 1.0000e+00, -3.3114e-09,  3.3114e-09],\n",
              "        [-3.3114e-09,  1.0000e+00,  6.6227e-09],\n",
              "        [ 3.3114e-09,  6.6227e-09,  1.0000e+00]])"
            ]
          },
          "metadata": {},
          "execution_count": 74
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "scM6FCpjNgYA"
      },
      "source": [
        "A pesar de los errores de redondeo que podemos ignorar con seguridad, esto confirma que $K^TK = I$ y por lo tanto $K$ es una matriz ortogonal."
      ]
    }
  ]
}