{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import numpy as np"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[0, 1, 2], [3, 4, 5]]\n",
      "<class 'list'>\n"
     ]
    }
   ],
   "source": [
    "l_2d = [[0, 1, 2], [3, 4, 5]]\n",
    "\n",
    "print(l_2d)\n",
    "print(type(l_2d))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[0 1 2]\n",
      " [3 4 5]]\n",
      "<class 'numpy.ndarray'>\n"
     ]
    }
   ],
   "source": [
    "arr = np.array([[0, 1, 2], [3, 4, 5]])\n",
    "\n",
    "print(arr)\n",
    "print(type(arr))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[0 1 2 3 4 5]\n"
     ]
    }
   ],
   "source": [
    "arr = np.arange(6)\n",
    "\n",
    "print(arr)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[0 1 2]\n",
      " [3 4 5]]\n"
     ]
    }
   ],
   "source": [
    "arr = np.arange(6).reshape((2, 3))\n",
    "\n",
    "print(arr)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[0 1 2]\n",
      " [3 4 5]]\n",
      "<class 'numpy.matrixlib.defmatrix.matrix'>\n"
     ]
    }
   ],
   "source": [
    "mat = np.matrix([[0, 1, 2], [3, 4, 5]])\n",
    "\n",
    "print(mat)\n",
    "print(type(mat))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[0 1 2]\n",
      " [3 4 5]]\n",
      "<class 'numpy.matrixlib.defmatrix.matrix'>\n"
     ]
    }
   ],
   "source": [
    "mat = np.matrix(arr)\n",
    "\n",
    "print(mat)\n",
    "print(type(mat))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[0 1 2]]\n",
      "<class 'numpy.matrixlib.defmatrix.matrix'>\n",
      "(1, 3)\n"
     ]
    }
   ],
   "source": [
    "mat_1d = np.matrix([0, 1, 2])\n",
    "\n",
    "print(mat_1d)\n",
    "print(type(mat_1d))\n",
    "print(mat_1d.shape)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# mat_3d = np.matrix([[[0, 1, 2]]])\n",
    "# ValueError: matrix must be 2-dimensional"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1\n"
     ]
    }
   ],
   "source": [
    "print(l_2d[0][1])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[0, 100, 2], [3, 4, 5]]\n"
     ]
    }
   ],
   "source": [
    "l_2d[0][1] = 100\n",
    "\n",
    "print(l_2d)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1\n"
     ]
    }
   ],
   "source": [
    "print(arr[0][1])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1\n"
     ]
    }
   ],
   "source": [
    "print(arr[0, 1])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[  0 100   2]\n",
      " [  3   4   5]]\n"
     ]
    }
   ],
   "source": [
    "arr[0, 1] = 100\n",
    "\n",
    "print(arr)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[0, 1, 2], [3, 4, 5]]\n"
     ]
    }
   ],
   "source": [
    "l_2d = [[0, 1, 2], [3, 4, 5]]\n",
    "\n",
    "print(l_2d)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[0, 3], [1, 4], [2, 5]]\n"
     ]
    }
   ],
   "source": [
    "l_2d_t = [list(x) for x in list(zip(*l_2d))]\n",
    "print(l_2d_t)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[0 1 2]\n",
      " [3 4 5]]\n"
     ]
    }
   ],
   "source": [
    "arr = np.arange(6).reshape((2, 3))\n",
    "\n",
    "print(arr)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[0 3]\n",
      " [1 4]\n",
      " [2 5]]\n"
     ]
    }
   ],
   "source": [
    "arr_t = arr.T\n",
    "\n",
    "print(arr_t)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "l_2d_1 = [[0, 1, 2], [3, 4, 5]]\n",
    "l_2d_2 = [[0, 2, 4], [6, 8, 10]]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[0, 1, 2], [3, 4, 5], [0, 2, 4], [6, 8, 10]]\n"
     ]
    }
   ],
   "source": [
    "l_2d_sum = l_2d_1 + l_2d_2\n",
    "\n",
    "print(l_2d_sum)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# l_2d_sub = l_2d_1 - l_2d_2\n",
    "# TypeError: unsupported operand type(s) for -: 'list' and 'list'"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[0 1 2]\n",
      " [3 4 5]]\n"
     ]
    }
   ],
   "source": [
    "arr1 = np.arange(6).reshape((2, 3))\n",
    "\n",
    "print(arr1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[ 0  2  4]\n",
      " [ 6  8 10]]\n"
     ]
    }
   ],
   "source": [
    "arr2 = np.arange(0, 12, 2).reshape((2, 3))\n",
    "\n",
    "print(arr2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[ 0  3  6]\n",
      " [ 9 12 15]]\n"
     ]
    }
   ],
   "source": [
    "arr_sum = arr1 + arr2\n",
    "\n",
    "print(arr_sum)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[ 0 -1 -2]\n",
      " [-3 -4 -5]]\n"
     ]
    }
   ],
   "source": [
    "arr_sub = arr1 - arr2\n",
    "\n",
    "print(arr_sub)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "mat1 = np.matrix(arr1)\n",
    "mat2 = np.matrix(arr2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[ 0  3  6]\n",
      " [ 9 12 15]]\n"
     ]
    }
   ],
   "source": [
    "mat_sum = mat1 + mat2\n",
    "\n",
    "print(mat_sum)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[ 0 -1 -2]\n",
      " [-3 -4 -5]]\n"
     ]
    }
   ],
   "source": [
    "mat_sub = mat1 - mat2\n",
    "\n",
    "print(mat_sub)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[0, 1, 2], [3, 4, 5], [0, 1, 2], [3, 4, 5]]\n"
     ]
    }
   ],
   "source": [
    "l_2d_mul = l_2d_1 * 2\n",
    "\n",
    "print(l_2d_mul)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# l_2d_mul = l_2d_1 * l_2d_2\n",
    "# TypeError: can't multiply sequence by non-int of type 'list'"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[ 0  2  4]\n",
      " [ 6  8 10]]\n"
     ]
    }
   ],
   "source": [
    "arr_mul = arr1 * 2\n",
    "\n",
    "print(arr_mul)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[ 0  2  4]\n",
      " [ 6  8 10]]\n"
     ]
    }
   ],
   "source": [
    "mat_mul = mat1 * 2\n",
    "\n",
    "print(mat_mul)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[ 0  2  8]\n",
      " [18 32 50]]\n"
     ]
    }
   ],
   "source": [
    "arr_mul = np.multiply(arr1, arr2)\n",
    "\n",
    "print(arr_mul)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[ 0  2  8]\n",
      " [18 32 50]]\n"
     ]
    }
   ],
   "source": [
    "mat_mul = np.multiply(mat1, mat2)\n",
    "\n",
    "print(mat_mul)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[ 0  2  8]\n",
      " [18 32 50]]\n"
     ]
    }
   ],
   "source": [
    "arr_mul = arr1 * arr2\n",
    "\n",
    "print(arr_mul)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[0 1]\n",
      " [2 3]]\n"
     ]
    }
   ],
   "source": [
    "arr1 = np.arange(4).reshape((2, 2))\n",
    "\n",
    "print(arr1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[0 1 2]\n",
      " [3 4 5]]\n"
     ]
    }
   ],
   "source": [
    "arr2 = np.arange(6).reshape((2, 3))\n",
    "\n",
    "print(arr2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[ 3  4  5]\n",
      " [ 9 14 19]]\n"
     ]
    }
   ],
   "source": [
    "arr_mul_matrix = np.dot(arr1, arr2)\n",
    "\n",
    "print(arr_mul_matrix)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[ 3  4  5]\n",
      " [ 9 14 19]]\n"
     ]
    }
   ],
   "source": [
    "arr_mul_matrix = arr1.dot(arr2)\n",
    "\n",
    "print(arr_mul_matrix)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[ 3  4  5]\n",
      " [ 9 14 19]]\n"
     ]
    }
   ],
   "source": [
    "arr_mul_matrix = np.matmul(arr1, arr2)\n",
    "\n",
    "print(arr_mul_matrix)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[ 3  4  5]\n",
      " [ 9 14 19]]\n"
     ]
    }
   ],
   "source": [
    "arr_mul_matrix = arr1 @ arr2\n",
    "\n",
    "print(arr_mul_matrix)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "mat1 = np.matrix(arr1)\n",
    "mat2 = np.matrix(arr2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[ 3  4  5]\n",
      " [ 9 14 19]]\n"
     ]
    }
   ],
   "source": [
    "mat_mul_matrix = np.dot(mat1, mat2)\n",
    "\n",
    "print(mat_mul_matrix)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[ 3  4  5]\n",
      " [ 9 14 19]]\n"
     ]
    }
   ],
   "source": [
    "mat_mul_matrix = mat1.dot(mat2)\n",
    "\n",
    "print(mat_mul_matrix)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[ 3  4  5]\n",
      " [ 9 14 19]]\n"
     ]
    }
   ],
   "source": [
    "mat_mul_matrix = np.matmul(mat1, mat2)\n",
    "\n",
    "print(mat_mul_matrix)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[ 3  4  5]\n",
      " [ 9 14 19]]\n"
     ]
    }
   ],
   "source": [
    "mat_mul_matrix = mat1 @ mat2\n",
    "\n",
    "print(mat_mul_matrix)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[ 3  4  5]\n",
      " [ 9 14 19]]\n"
     ]
    }
   ],
   "source": [
    "mat_mul_matrix = mat1 * mat2\n",
    "\n",
    "print(mat_mul_matrix)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[1 2]\n",
      " [3 4]]\n"
     ]
    }
   ],
   "source": [
    "arr = np.arange(1, 5).reshape(2, 2)\n",
    "\n",
    "print(arr)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[ 1  4]\n",
      " [ 9 16]]\n"
     ]
    }
   ],
   "source": [
    "arr_p = arr**2\n",
    "\n",
    "print(arr_p)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[1 2]\n",
      " [3 4]]\n"
     ]
    }
   ],
   "source": [
    "mat = np.matrix(arr)\n",
    "\n",
    "print(mat)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[ 7 10]\n",
      " [15 22]]\n"
     ]
    }
   ],
   "source": [
    "mat_p = mat**2\n",
    "\n",
    "print(mat_p)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[ True  True]\n",
      " [ True  True]]\n"
     ]
    }
   ],
   "source": [
    "print(mat**2 == mat * mat)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[ True  True]\n",
      " [ True  True]]\n"
     ]
    }
   ],
   "source": [
    "print(mat**3 == mat * mat * mat)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# arr_n = arr**-1\n",
    "# ValueError: Integers to negative integer powers are not allowed."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[1.         0.5       ]\n",
      " [0.33333333 0.25      ]]\n"
     ]
    }
   ],
   "source": [
    "arr_f = np.array(arr, dtype=float)\n",
    "\n",
    "arr_f_n = arr_f**-1\n",
    "\n",
    "print(arr_f_n)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[-2.   1. ]\n",
      " [ 1.5 -0.5]]\n"
     ]
    }
   ],
   "source": [
    "mat_inv = mat**-1\n",
    "\n",
    "print(mat_inv)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[ 5.5  -2.5 ]\n",
      " [-3.75  1.75]]\n"
     ]
    }
   ],
   "source": [
    "mat_inv2 = mat**-2\n",
    "\n",
    "print(mat_inv2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[ True  True]\n",
      " [ True  True]]\n"
     ]
    }
   ],
   "source": [
    "print(mat**-2 == mat**-1 * mat**-1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[ True  True]\n",
      " [ True  True]]\n"
     ]
    }
   ],
   "source": [
    "print(mat**-3 == mat**-1 * mat**-1 * mat**-1)"
   ]
  }
 ],
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