Linear_Algebra.ipynb

{
  "cells": [
    {
      "cell_type": "markdown",
      "source": [
        "# Linear Algebra"
      ],
      "metadata": {}
    },
    {
      "cell_type": "code",
      "source": [
        "# Library\n",
        "import numpy as np"
      ],
      "outputs": [],
      "execution_count": 1,
      "metadata": {
        "collapsed": false,
        "outputHidden": false,
        "inputHidden": false
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "### Matrices"
      ],
      "metadata": {}
    },
    {
      "cell_type": "code",
      "source": [
        "matrices = np.array([[1,2,3],[-4,5,6]])"
      ],
      "outputs": [],
      "execution_count": 2,
      "metadata": {
        "collapsed": false,
        "outputHidden": false,
        "inputHidden": false
      }
    },
    {
      "cell_type": "code",
      "source": [
        "matrices"
      ],
      "outputs": [
        {
          "output_type": "execute_result",
          "execution_count": 3,
          "data": {
            "text/plain": [
              "array([[ 1,  2,  3],\n",
              "       [-4,  5,  6]])"
            ]
          },
          "metadata": {}
        }
      ],
      "execution_count": 3,
      "metadata": {
        "collapsed": false,
        "outputHidden": false,
        "inputHidden": false
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "### Scalars"
      ],
      "metadata": {}
    },
    {
      "cell_type": "code",
      "source": [
        "scalars = 8\n"
      ],
      "outputs": [],
      "execution_count": 4,
      "metadata": {
        "collapsed": false,
        "outputHidden": false,
        "inputHidden": false
      }
    },
    {
      "cell_type": "code",
      "source": [
        "scalars"
      ],
      "outputs": [
        {
          "output_type": "execute_result",
          "execution_count": 5,
          "data": {
            "text/plain": [
              "8"
            ]
          },
          "metadata": {}
        }
      ],
      "execution_count": 5,
      "metadata": {
        "collapsed": false,
        "outputHidden": false,
        "inputHidden": false
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "### Scalar Array"
      ],
      "metadata": {}
    },
    {
      "cell_type": "code",
      "source": [
        "s_array = np.array(5)"
      ],
      "outputs": [],
      "execution_count": 6,
      "metadata": {
        "collapsed": false,
        "outputHidden": false,
        "inputHidden": false
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "### Vectors"
      ],
      "metadata": {}
    },
    {
      "cell_type": "code",
      "source": [
        "vectors = np.array([7,-8,0])"
      ],
      "outputs": [],
      "execution_count": 7,
      "metadata": {
        "collapsed": false,
        "outputHidden": false,
        "inputHidden": false
      }
    },
    {
      "cell_type": "code",
      "source": [
        "vectors"
      ],
      "outputs": [
        {
          "output_type": "execute_result",
          "execution_count": 8,
          "data": {
            "text/plain": [
              "array([ 7, -8,  0])"
            ]
          },
          "metadata": {}
        }
      ],
      "execution_count": 8,
      "metadata": {
        "collapsed": false,
        "outputHidden": false,
        "inputHidden": false
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "## Data Types"
      ],
      "metadata": {}
    },
    {
      "cell_type": "code",
      "source": [
        "type(matrices)"
      ],
      "outputs": [
        {
          "output_type": "execute_result",
          "execution_count": 9,
          "data": {
            "text/plain": [
              "numpy.ndarray"
            ]
          },
          "metadata": {}
        }
      ],
      "execution_count": 9,
      "metadata": {
        "collapsed": false,
        "outputHidden": false,
        "inputHidden": false
      }
    },
    {
      "cell_type": "code",
      "source": [
        "type(scalars)"
      ],
      "outputs": [
        {
          "output_type": "execute_result",
          "execution_count": 10,
          "data": {
            "text/plain": [
              "int"
            ]
          },
          "metadata": {}
        }
      ],
      "execution_count": 10,
      "metadata": {
        "collapsed": false,
        "outputHidden": false,
        "inputHidden": false
      }
    },
    {
      "cell_type": "code",
      "source": [
        "type(vectors)"
      ],
      "outputs": [
        {
          "output_type": "execute_result",
          "execution_count": 11,
          "data": {
            "text/plain": [
              "numpy.ndarray"
            ]
          },
          "metadata": {}
        }
      ],
      "execution_count": 11,
      "metadata": {
        "collapsed": false,
        "outputHidden": false,
        "inputHidden": false
      }
    },
    {
      "cell_type": "code",
      "source": [
        "type(s_array)"
      ],
      "outputs": [
        {
          "output_type": "execute_result",
          "execution_count": 12,
          "data": {
            "text/plain": [
              "numpy.ndarray"
            ]
          },
          "metadata": {}
        }
      ],
      "execution_count": 12,
      "metadata": {
        "collapsed": false,
        "outputHidden": false,
        "inputHidden": false
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "## Data Shapes"
      ],
      "metadata": {}
    },
    {
      "cell_type": "code",
      "source": [
        "matrices.shape"
      ],
      "outputs": [
        {
          "output_type": "execute_result",
          "execution_count": 13,
          "data": {
            "text/plain": [
              "(2, 3)"
            ]
          },
          "metadata": {}
        }
      ],
      "execution_count": 13,
      "metadata": {
        "collapsed": false,
        "outputHidden": false,
        "inputHidden": false
      }
    },
    {
      "cell_type": "code",
      "source": [
        "scalars.shape"
      ],
      "outputs": [
        {
          "output_type": "error",
          "ename": "AttributeError",
          "evalue": "'int' object has no attribute 'shape'",
          "traceback": [
            "\u001b[1;31m---------------------------------------------------------------------------\u001b[0m",
            "\u001b[1;31mAttributeError\u001b[0m                            Traceback (most recent call last)",
            "\u001b[1;32m<ipython-input-14-818a7e2b7fe2>\u001b[0m in \u001b[0;36m<module>\u001b[1;34m()\u001b[0m\n\u001b[1;32m----> 1\u001b[1;33m \u001b[0mscalars\u001b[0m\u001b[1;33m.\u001b[0m\u001b[0mshape\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m",
            "\u001b[1;31mAttributeError\u001b[0m: 'int' object has no attribute 'shape'"
          ]
        }
      ],
      "execution_count": 14,
      "metadata": {
        "collapsed": false,
        "outputHidden": false,
        "inputHidden": false
      }
    },
    {
      "cell_type": "code",
      "source": [
        "vectors.shape"
      ],
      "outputs": [
        {
          "output_type": "execute_result",
          "execution_count": 15,
          "data": {
            "text/plain": [
              "(3,)"
            ]
          },
          "metadata": {}
        }
      ],
      "execution_count": 15,
      "metadata": {
        "collapsed": false,
        "outputHidden": false,
        "inputHidden": false
      }
    },
    {
      "cell_type": "code",
      "source": [
        "s_array.shape"
      ],
      "outputs": [
        {
          "output_type": "execute_result",
          "execution_count": 16,
          "data": {
            "text/plain": [
              "()"
            ]
          },
          "metadata": {}
        }
      ],
      "execution_count": 16,
      "metadata": {
        "collapsed": false,
        "outputHidden": false,
        "inputHidden": false
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "## Creating a column vector"
      ],
      "metadata": {}
    },
    {
      "cell_type": "code",
      "source": [
        "vectors.reshape(1,3)"
      ],
      "outputs": [
        {
          "output_type": "execute_result",
          "execution_count": 17,
          "data": {
            "text/plain": [
              "array([[ 7, -8,  0]])"
            ]
          },
          "metadata": {}
        }
      ],
      "execution_count": 17,
      "metadata": {
        "collapsed": false,
        "outputHidden": false,
        "inputHidden": false
      }
    },
    {
      "cell_type": "code",
      "source": [
        "vectors.reshape(3,1)"
      ],
      "outputs": [
        {
          "output_type": "execute_result",
          "execution_count": 18,
          "data": {
            "text/plain": [
              "array([[ 7],\n",
              "       [-8],\n",
              "       [ 0]])"
            ]
          },
          "metadata": {}
        }
      ],
      "execution_count": 18,
      "metadata": {
        "collapsed": false,
        "outputHidden": false,
        "inputHidden": false
      }
    },
    {
      "cell_type": "code",
      "source": [
        "matrices + scalars"
      ],
      "outputs": [
        {
          "output_type": "execute_result",
          "execution_count": 19,
          "data": {
            "text/plain": [
              "array([[ 9, 10, 11],\n",
              "       [ 4, 13, 14]])"
            ]
          },
          "metadata": {}
        }
      ],
      "execution_count": 19,
      "metadata": {
        "collapsed": false,
        "outputHidden": false,
        "inputHidden": false
      }
    },
    {
      "cell_type": "code",
      "source": [
        "matrices + s_array"
      ],
      "outputs": [
        {
          "output_type": "execute_result",
          "execution_count": 20,
          "data": {
            "text/plain": [
              "array([[ 6,  7,  8],\n",
              "       [ 1, 10, 11]])"
            ]
          },
          "metadata": {}
        }
      ],
      "execution_count": 20,
      "metadata": {
        "collapsed": false,
        "outputHidden": false,
        "inputHidden": false
      }
    },
    {
      "cell_type": "code",
      "source": [
        "vectors + scalars"
      ],
      "outputs": [
        {
          "output_type": "execute_result",
          "execution_count": 21,
          "data": {
            "text/plain": [
              "array([15,  0,  8])"
            ]
          },
          "metadata": {}
        }
      ],
      "execution_count": 21,
      "metadata": {
        "collapsed": false,
        "outputHidden": false,
        "inputHidden": false
      }
    },
    {
      "cell_type": "code",
      "source": [
        "vectors + s_array"
      ],
      "outputs": [
        {
          "output_type": "execute_result",
          "execution_count": 22,
          "data": {
            "text/plain": [
              "array([12, -3,  5])"
            ]
          },
          "metadata": {}
        }
      ],
      "execution_count": 22,
      "metadata": {
        "collapsed": false,
        "outputHidden": false,
        "inputHidden": false
      }
    },
    {
      "cell_type": "code",
      "source": [
        "matrices + vectors"
      ],
      "outputs": [
        {
          "output_type": "execute_result",
          "execution_count": 23,
          "data": {
            "text/plain": [
              "array([[ 8, -6,  3],\n",
              "       [ 3, -3,  6]])"
            ]
          },
          "metadata": {}
        }
      ],
      "execution_count": 23,
      "metadata": {
        "collapsed": false,
        "outputHidden": false,
        "inputHidden": false
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "# Tensors"
      ],
      "metadata": {}
    },
    {
      "cell_type": "code",
      "source": [
        "m1 = np.array([[1,2,3],[-4,-5,-6]])\n",
        "m1"
      ],
      "outputs": [
        {
          "output_type": "execute_result",
          "execution_count": 24,
          "data": {
            "text/plain": [
              "array([[ 1,  2,  3],\n",
              "       [-4, -5, -6]])"
            ]
          },
          "metadata": {}
        }
      ],
      "execution_count": 24,
      "metadata": {
        "collapsed": false,
        "outputHidden": false,
        "inputHidden": false
      }
    },
    {
      "cell_type": "code",
      "source": [
        "m2 = np.array([[7,8,9],[0,1,2]])\n",
        "m2"
      ],
      "outputs": [
        {
          "output_type": "execute_result",
          "execution_count": 25,
          "data": {
            "text/plain": [
              "array([[7, 8, 9],\n",
              "       [0, 1, 2]])"
            ]
          },
          "metadata": {}
        }
      ],
      "execution_count": 25,
      "metadata": {
        "collapsed": false,
        "outputHidden": false,
        "inputHidden": false
      }
    },
    {
      "cell_type": "code",
      "source": [
        "t = np.array([m1,m2])\n",
        "t"
      ],
      "outputs": [
        {
          "output_type": "execute_result",
          "execution_count": 26,
          "data": {
            "text/plain": [
              "array([[[ 1,  2,  3],\n",
              "        [-4, -5, -6]],\n",
              "\n",
              "       [[ 7,  8,  9],\n",
              "        [ 0,  1,  2]]])"
            ]
          },
          "metadata": {}
        }
      ],
      "execution_count": 26,
      "metadata": {
        "collapsed": false,
        "outputHidden": false,
        "inputHidden": false
      }
    },
    {
      "cell_type": "code",
      "source": [
        "t.shape"
      ],
      "outputs": [
        {
          "output_type": "execute_result",
          "execution_count": 27,
          "data": {
            "text/plain": [
              "(2, 2, 3)"
            ]
          },
          "metadata": {}
        }
      ],
      "execution_count": 27,
      "metadata": {
        "collapsed": false,
        "outputHidden": false,
        "inputHidden": false
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "## Create Tensor"
      ],
      "metadata": {}
    },
    {
      "cell_type": "code",
      "source": [
        "tensor = np.array([[[ 1, 2, 3], [4, 5, 6]], [[ 7,  8,  9], [ -3,  -2, -1]]])"
      ],
      "outputs": [],
      "execution_count": 28,
      "metadata": {
        "collapsed": false,
        "outputHidden": false,
        "inputHidden": false
      }
    },
    {
      "cell_type": "code",
      "source": [
        "tensor"
      ],
      "outputs": [
        {
          "output_type": "execute_result",
          "execution_count": 29,
          "data": {
            "text/plain": [
              "array([[[ 1,  2,  3],\n",
              "        [ 4,  5,  6]],\n",
              "\n",
              "       [[ 7,  8,  9],\n",
              "        [-3, -2, -1]]])"
            ]
          },
          "metadata": {}
        }
      ],
      "execution_count": 29,
      "metadata": {
        "collapsed": false,
        "outputHidden": false,
        "inputHidden": false
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "## Addition Matrices"
      ],
      "metadata": {}
    },
    {
      "cell_type": "code",
      "source": [
        "m1 + m2"
      ],
      "outputs": [
        {
          "output_type": "execute_result",
          "execution_count": 30,
          "data": {
            "text/plain": [
              "array([[ 8, 10, 12],\n",
              "       [-4, -4, -4]])"
            ]
          },
          "metadata": {}
        }
      ],
      "execution_count": 30,
      "metadata": {
        "collapsed": false,
        "outputHidden": false,
        "inputHidden": false
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "## Subtraction Matrices"
      ],
      "metadata": {}
    },
    {
      "cell_type": "code",
      "source": [
        "m1 - m2"
      ],
      "outputs": [
        {
          "output_type": "execute_result",
          "execution_count": 31,
          "data": {
            "text/plain": [
              "array([[-6, -6, -6],\n",
              "       [-4, -6, -8]])"
            ]
          },
          "metadata": {}
        }
      ],
      "execution_count": 31,
      "metadata": {
        "collapsed": false,
        "outputHidden": false,
        "inputHidden": false
      }
    },
    {
      "cell_type": "code",
      "source": [
        "m3 = np.array([[8,10],[11,12],[15,18]])\n",
        "m3"
      ],
      "outputs": [
        {
          "output_type": "execute_result",
          "execution_count": 32,
          "data": {
            "text/plain": [
              "array([[ 8, 10],\n",
              "       [11, 12],\n",
              "       [15, 18]])"
            ]
          },
          "metadata": {}
        }
      ],
      "execution_count": 32,
      "metadata": {
        "collapsed": false,
        "outputHidden": false,
        "inputHidden": false
      }
    },
    {
      "cell_type": "code",
      "source": [
        "m4 = np.array([[6,8],[-5,10],[-18,20]])\n",
        "m4"
      ],
      "outputs": [
        {
          "output_type": "execute_result",
          "execution_count": 33,
          "data": {
            "text/plain": [
              "array([[  6,   8],\n",
              "       [ -5,  10],\n",
              "       [-18,  20]])"
            ]
          },
          "metadata": {}
        }
      ],
      "execution_count": 33,
      "metadata": {
        "collapsed": false,
        "outputHidden": false,
        "inputHidden": false
      }
    },
    {
      "cell_type": "code",
      "source": [
        "m3 - m4"
      ],
      "outputs": [
        {
          "output_type": "execute_result",
          "execution_count": 34,
          "data": {
            "text/plain": [
              "array([[ 2,  2],\n",
              "       [16,  2],\n",
              "       [33, -2]])"
            ]
          },
          "metadata": {}
        }
      ],
      "execution_count": 34,
      "metadata": {
        "collapsed": false,
        "outputHidden": false,
        "inputHidden": false
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "## Addition Vectors"
      ],
      "metadata": {}
    },
    {
      "cell_type": "code",
      "source": [
        "v1 = np.array([1,2,3,4,5])\n",
        "v2 = np.array([5,4,3,2,1])"
      ],
      "outputs": [],
      "execution_count": 35,
      "metadata": {
        "collapsed": false,
        "outputHidden": false,
        "inputHidden": false
      }
    },
    {
      "cell_type": "code",
      "source": [
        "v1 + v2"
      ],
      "outputs": [
        {
          "output_type": "execute_result",
          "execution_count": 36,
          "data": {
            "text/plain": [
              "array([6, 6, 6, 6, 6])"
            ]
          },
          "metadata": {}
        }
      ],
      "execution_count": 36,
      "metadata": {
        "collapsed": false,
        "outputHidden": false,
        "inputHidden": false
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "## Subtraction Vectors"
      ],
      "metadata": {}
    },
    {
      "cell_type": "code",
      "source": [
        "v1 - v2"
      ],
      "outputs": [
        {
          "output_type": "execute_result",
          "execution_count": 37,
          "data": {
            "text/plain": [
              "array([-4, -2,  0,  2,  4])"
            ]
          },
          "metadata": {}
        }
      ],
      "execution_count": 37,
      "metadata": {
        "collapsed": false,
        "outputHidden": false,
        "inputHidden": false
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "## Exceptions (addition with a scalar)"
      ],
      "metadata": {}
    },
    {
      "cell_type": "code",
      "source": [
        "m1 + 1"
      ],
      "outputs": [
        {
          "output_type": "execute_result",
          "execution_count": 38,
          "data": {
            "text/plain": [
              "array([[ 2,  3,  4],\n",
              "       [-3, -4, -5]])"
            ]
          },
          "metadata": {}
        }
      ],
      "execution_count": 38,
      "metadata": {
        "collapsed": false,
        "outputHidden": false,
        "inputHidden": false
      }
    },
    {
      "cell_type": "code",
      "source": [
        "v1 + 1"
      ],
      "outputs": [
        {
          "output_type": "execute_result",
          "execution_count": 39,
          "data": {
            "text/plain": [
              "array([2, 3, 4, 5, 6])"
            ]
          },
          "metadata": {}
        }
      ],
      "execution_count": 39,
      "metadata": {
        "collapsed": false,
        "outputHidden": false,
        "inputHidden": false
      }
    },
    {
      "cell_type": "code",
      "source": [
        "m1 + np.array([1])"
      ],
      "outputs": [
        {
          "output_type": "execute_result",
          "execution_count": 40,
          "data": {
            "text/plain": [
              "array([[ 2,  3,  4],\n",
              "       [-3, -4, -5]])"
            ]
          },
          "metadata": {}
        }
      ],
      "execution_count": 40,
      "metadata": {
        "collapsed": false,
        "outputHidden": false,
        "inputHidden": false
      }
    },
    {
      "cell_type": "code",
      "source": [
        "v1 + np.array([1])"
      ],
      "outputs": [
        {
          "output_type": "execute_result",
          "execution_count": 41,
          "data": {
            "text/plain": [
              "array([2, 3, 4, 5, 6])"
            ]
          },
          "metadata": {}
        }
      ],
      "execution_count": 41,
      "metadata": {
        "collapsed": false,
        "outputHidden": false,
        "inputHidden": false
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "## Transposing Matrices"
      ],
      "metadata": {}
    },
    {
      "cell_type": "code",
      "source": [
        "A = np.array([[1,3,5],[2,4,6]])\n",
        "A"
      ],
      "outputs": [
        {
          "output_type": "execute_result",
          "execution_count": 42,
          "data": {
            "text/plain": [
              "array([[1, 3, 5],\n",
              "       [2, 4, 6]])"
            ]
          },
          "metadata": {}
        }
      ],
      "execution_count": 42,
      "metadata": {
        "collapsed": false,
        "outputHidden": false,
        "inputHidden": false
      }
    },
    {
      "cell_type": "code",
      "source": [
        "A.T"
      ],
      "outputs": [
        {
          "output_type": "execute_result",
          "execution_count": 43,
          "data": {
            "text/plain": [
              "array([[1, 2],\n",
              "       [3, 4],\n",
              "       [5, 6]])"
            ]
          },
          "metadata": {}
        }
      ],
      "execution_count": 43,
      "metadata": {
        "collapsed": false,
        "outputHidden": false,
        "inputHidden": false
      }
    },
    {
      "cell_type": "code",
      "source": [
        "B = np.array([[8,10],[-2,-6]])\n",
        "B"
      ],
      "outputs": [
        {
          "output_type": "execute_result",
          "execution_count": 44,
          "data": {
            "text/plain": [
              "array([[ 8, 10],\n",
              "       [-2, -6]])"
            ]
          },
          "metadata": {}
        }
      ],
      "execution_count": 44,
      "metadata": {
        "collapsed": false,
        "outputHidden": false,
        "inputHidden": false
      }
    },
    {
      "cell_type": "code",
      "source": [
        "B.T"
      ],
      "outputs": [
        {
          "output_type": "execute_result",
          "execution_count": 45,
          "data": {
            "text/plain": [
              "array([[ 8, -2],\n",
              "       [10, -6]])"
            ]
          },
          "metadata": {}
        }
      ],
      "execution_count": 45,
      "metadata": {
        "collapsed": false,
        "outputHidden": false,
        "inputHidden": false
      }
    },
    {
      "cell_type": "code",
      "source": [
        "C = np.array([[2,3],[8,6],[-1,-2],[20,2]])\n",
        "C"
      ],
      "outputs": [
        {
          "output_type": "execute_result",
          "execution_count": 46,
          "data": {
            "text/plain": [
              "array([[ 2,  3],\n",
              "       [ 8,  6],\n",
              "       [-1, -2],\n",
              "       [20,  2]])"
            ]
          },
          "metadata": {}
        }
      ],
      "execution_count": 46,
      "metadata": {
        "collapsed": false,
        "outputHidden": false,
        "inputHidden": false
      }
    },
    {
      "cell_type": "code",
      "source": [
        "C.T"
      ],
      "outputs": [
        {
          "output_type": "execute_result",
          "execution_count": 47,
          "data": {
            "text/plain": [
              "array([[ 2,  8, -1, 20],\n",
              "       [ 3,  6, -2,  2]])"
            ]
          },
          "metadata": {}
        }
      ],
      "execution_count": 47,
      "metadata": {
        "collapsed": false,
        "outputHidden": false,
        "inputHidden": false
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "## Transposing Scalars"
      ],
      "metadata": {}
    },
    {
      "cell_type": "code",
      "source": [
        "s = np.array([8])"
      ],
      "outputs": [],
      "execution_count": 48,
      "metadata": {
        "collapsed": false,
        "outputHidden": false,
        "inputHidden": false
      }
    },
    {
      "cell_type": "code",
      "source": [
        "s.T"
      ],
      "outputs": [
        {
          "output_type": "execute_result",
          "execution_count": 49,
          "data": {
            "text/plain": [
              "array([8])"
            ]
          },
          "metadata": {}
        }
      ],
      "execution_count": 49,
      "metadata": {
        "collapsed": false,
        "outputHidden": false,
        "inputHidden": false
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "## Transposing Vectors"
      ],
      "metadata": {}
    },
    {
      "cell_type": "code",
      "source": [
        "v = np.array([1,2,3])\n",
        "v"
      ],
      "outputs": [
        {
          "output_type": "execute_result",
          "execution_count": 50,
          "data": {
            "text/plain": [
              "array([1, 2, 3])"
            ]
          },
          "metadata": {}
        }
      ],
      "execution_count": 50,
      "metadata": {
        "collapsed": false,
        "outputHidden": false,
        "inputHidden": false
      }
    },
    {
      "cell_type": "code",
      "source": [
        "v.T"
      ],
      "outputs": [
        {
          "output_type": "execute_result",
          "execution_count": 51,
          "data": {
            "text/plain": [
              "array([1, 2, 3])"
            ]
          },
          "metadata": {}
        }
      ],
      "execution_count": 51,
      "metadata": {
        "collapsed": false,
        "outputHidden": false,
        "inputHidden": false
      }
    },
    {
      "cell_type": "code",
      "source": [
        "v.shape"
      ],
      "outputs": [
        {
          "output_type": "execute_result",
          "execution_count": 52,
          "data": {
            "text/plain": [
              "(3,)"
            ]
          },
          "metadata": {}
        }
      ],
      "execution_count": 52,
      "metadata": {
        "collapsed": false,
        "outputHidden": false,
        "inputHidden": false
      }
    },
    {
      "cell_type": "code",
      "source": [
        "v_reshaped = v.reshape(1,3)\n",
        "v_reshaped"
      ],
      "outputs": [
        {
          "output_type": "execute_result",
          "execution_count": 53,
          "data": {
            "text/plain": [
              "array([[1, 2, 3]])"
            ]
          },
          "metadata": {}
        }
      ],
      "execution_count": 53,
      "metadata": {
        "collapsed": false,
        "outputHidden": false,
        "inputHidden": false
      }
    },
    {
      "cell_type": "code",
      "source": [
        "v_reshaped.T"
      ],
      "outputs": [
        {
          "output_type": "execute_result",
          "execution_count": 54,
          "data": {
            "text/plain": [
              "array([[1],\n",
              "       [2],\n",
              "       [3]])"
            ]
          },
          "metadata": {}
        }
      ],
      "execution_count": 54,
      "metadata": {
        "collapsed": false,
        "outputHidden": false,
        "inputHidden": false
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "## Dot Product"
      ],
      "metadata": {}
    },
    {
      "cell_type": "code",
      "source": [
        "x = np.array([1,2,3])\n",
        "y = np.array([4,5,6])"
      ],
      "outputs": [],
      "execution_count": 55,
      "metadata": {
        "collapsed": false,
        "outputHidden": false,
        "inputHidden": false
      }
    },
    {
      "cell_type": "code",
      "source": [
        "np.dot(x,y)"
      ],
      "outputs": [
        {
          "output_type": "execute_result",
          "execution_count": 56,
          "data": {
            "text/plain": [
              "32"
            ]
          },
          "metadata": {}
        }
      ],
      "execution_count": 56,
      "metadata": {
        "collapsed": false,
        "outputHidden": false,
        "inputHidden": false
      }
    },
    {
      "cell_type": "code",
      "source": [
        "u = np.array([0,2,4,6])\n",
        "v = np.array([-3,-2,-1,0])"
      ],
      "outputs": [],
      "execution_count": 57,
      "metadata": {
        "collapsed": false,
        "outputHidden": false,
        "inputHidden": false
      }
    },
    {
      "cell_type": "code",
      "source": [
        "np.dot(u,v)"
      ],
      "outputs": [
        {
          "output_type": "execute_result",
          "execution_count": 58,
          "data": {
            "text/plain": [
              "-8"
            ]
          },
          "metadata": {}
        }
      ],
      "execution_count": 58,
      "metadata": {
        "collapsed": false,
        "outputHidden": false,
        "inputHidden": false
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "## Scalar * Scalar"
      ],
      "metadata": {}
    },
    {
      "cell_type": "code",
      "source": [
        "np.dot(2,4)"
      ],
      "outputs": [
        {
          "output_type": "execute_result",
          "execution_count": 59,
          "data": {
            "text/plain": [
              "8"
            ]
          },
          "metadata": {}
        }
      ],
      "execution_count": 59,
      "metadata": {
        "collapsed": false,
        "outputHidden": false,
        "inputHidden": false
      }
    },
    {
      "cell_type": "code",
      "source": [
        "np.dot(-1,7)"
      ],
      "outputs": [
        {
          "output_type": "execute_result",
          "execution_count": 60,
          "data": {
            "text/plain": [
              "-7"
            ]
          },
          "metadata": {}
        }
      ],
      "execution_count": 60,
      "metadata": {
        "collapsed": false,
        "outputHidden": false,
        "inputHidden": false
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "## Scalar * Vector"
      ],
      "metadata": {}
    },
    {
      "cell_type": "code",
      "source": [
        "x"
      ],
      "outputs": [
        {
          "output_type": "execute_result",
          "execution_count": 61,
          "data": {
            "text/plain": [
              "array([1, 2, 3])"
            ]
          },
          "metadata": {}
        }
      ],
      "execution_count": 61,
      "metadata": {
        "collapsed": false,
        "outputHidden": false,
        "inputHidden": false
      }
    },
    {
      "cell_type": "code",
      "source": [
        "5*x"
      ],
      "outputs": [
        {
          "output_type": "execute_result",
          "execution_count": 62,
          "data": {
            "text/plain": [
              "array([ 5, 10, 15])"
            ]
          },
          "metadata": {}
        }
      ],
      "execution_count": 62,
      "metadata": {
        "collapsed": false,
        "outputHidden": false,
        "inputHidden": false
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "## Scalar * Matrix"
      ],
      "metadata": {}
    },
    {
      "cell_type": "code",
      "source": [
        "3*A"
      ],
      "outputs": [
        {
          "output_type": "execute_result",
          "execution_count": 63,
          "data": {
            "text/plain": [
              "array([[ 3,  9, 15],\n",
              "       [ 6, 12, 18]])"
            ]
          },
          "metadata": {}
        }
      ],
      "execution_count": 63,
      "metadata": {
        "collapsed": false,
        "outputHidden": false,
        "inputHidden": false
      }
    },
    {
      "cell_type": "markdown",
      "source": [
        "## Matrix * Matrix"
      ],
      "metadata": {}
    },
    {
      "cell_type": "code",
      "source": [
        "A = np.array([[1,2,3],[9,8,7]])\n",
        "A"
      ],
      "outputs": [
        {
          "output_type": "execute_result",
          "execution_count": 64,
          "data": {
            "text/plain": [
              "array([[1, 2, 3],\n",
              "       [9, 8, 7]])"
            ]
          },
          "metadata": {}
        }
      ],
      "execution_count": 64,
      "metadata": {
        "collapsed": false,
        "outputHidden": false,
        "inputHidden": false
      }
    },
    {
      "cell_type": "code",
      "source": [
        "B = np.array([[2,4],[-8,-6],[3,5]])\n",
        "B"
      ],
      "outputs": [
        {
          "output_type": "execute_result",
          "execution_count": 65,
          "data": {
            "text/plain": [
              "array([[ 2,  4],\n",
              "       [-8, -6],\n",
              "       [ 3,  5]])"
            ]
          },
          "metadata": {}
        }
      ],
      "execution_count": 65,
      "metadata": {
        "collapsed": false,
        "outputHidden": false,
        "inputHidden": false
      }
    },
    {
      "cell_type": "code",
      "source": [
        "np.dot(A,B)"
      ],
      "outputs": [
        {
          "output_type": "execute_result",
          "execution_count": 66,
          "data": {
            "text/plain": [
              "array([[ -5,   7],\n",
              "       [-25,  23]])"
            ]
          },
          "metadata": {}
        }
      ],
      "execution_count": 66,
      "metadata": {
        "collapsed": false,
        "outputHidden": false,
        "inputHidden": false
      }
    }
  ],
  "metadata": {
    "kernel_info": {
      "name": "python3"
    },
    "language_info": {
      "file_extension": ".py",
      "nbconvert_exporter": "python",
      "version": "3.5.5",
      "mimetype": "text/x-python",
      "name": "python",
      "pygments_lexer": "ipython3",
      "codemirror_mode": {
        "version": 3,
        "name": "ipython"
      }
    },
    "kernelspec": {
      "name": "python3",
      "language": "python",
      "display_name": "Python 3"
    },
    "nteract": {
      "version": "0.14.5"
    }
  },
  "nbformat": 4,
  "nbformat_minor": 0
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