Linear Algebra.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<!DOCTYPE html>\n",
    "<html>\n",
    "<body>\n",
    "<div align=\"center\">\n",
    "<h3>Prepared by Asif Bhat</h3>\n",
    "    \n",
    "<h1>Linear Algebra with Python</h1>\n",
    "\n",
    "<h3>Follow Me on - <a href=\"https://www.linkedin.com/in/asif-bhat/\">LinkedIn</a>&nbsp; <a href=\"https://mobile.twitter.com/_asifbhat_\">Twitter</a>&nbsp; <a href=\"https://www.instagram.com/datasciencescoop/?hl=en\">Instagram</a>&nbsp; <a href=\"https://www.facebook.com/datasciencescoop/\">Facebook</a></h3>\n",
    "</div>\n",
    "</body>\n",
    "</html>\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Linear Algebra"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from mpl_toolkits.mplot3d import Axes3D"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [],
   "source": [
    "v = [3,4]\n",
    "u = [1,2,3]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "([3, 4], [1, 2, 3])"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "v ,u"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "list"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "type(v)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [],
   "source": [
    "w = np.array([9,5,7])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "numpy.ndarray"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "type(w)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "3"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "w.shape[0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(3,)"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "w.shape"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Reading elements from an array "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [],
   "source": [
    "a = np.array([7,5,3,9,0,2])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "7"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a[0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([5, 3, 9, 0, 2])"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a[1:]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([5, 3, 9])"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a[1:4]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a[-1]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "9"
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a[-3]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "7"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a[-6]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([9, 0])"
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "a[-3:-1]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Plotting a Vector"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "What is vector : https://www.youtube.com/watch?v=fNk_zzaMoSs&list=PLZHQObOWTQDPD3MizzM2xVFitgF8hE_ab&index=1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [],
   "source": [
    "v = [3,4]\n",
    "u = [1,2,3]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x1ec68a84d68>]"
      ]
     },
     "execution_count": 33,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot (v)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x1ec68b11f98>]"
      ]
     },
     "execution_count": 34,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot([0,v[0]] , [0,v[1]])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Plot 2D Vector"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot([0,v[0]] , [0,v[1]])\n",
    "plt.plot([8,-8] , [0,0] , 'k--')\n",
    "plt.plot([0,0] , [8,-8] , 'k--')\n",
    "plt.grid()\n",
    "plt.axis((-8, 8, -8, 8))\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Plot the 3D vector"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure()\n",
    "ax = Axes3D(fig)\n",
    "ax.plot([0,u[0]],[0,u[1]],[0,u[2]])\n",
    "plt.axis('equal')\n",
    "ax.plot([0, 0],[0, 0],[-5, 5],'k--')\n",
    "ax.plot([0, 0],[-5, 5],[0, 0],'k--')\n",
    "ax.plot([-5, 5],[0, 0],[0, 0],'k--')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Vector Addition"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "V3 = [4 6]\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "v1 = np.array([1,2])\n",
    "v2 = np.array([3,4])\n",
    "v3 = v1+v2\n",
    "v3 = np.add(v1,v2)\n",
    "print('V3 =' ,v3)\n",
    "plt.plot([0,v1[0]] , [0,v1[1]] , 'r' , label = 'v1')\n",
    "plt.plot([0,v2[0]] , [0,v2[1]], 'b' , label = 'v2')\n",
    "plt.plot([0,v3[0]] , [0,v3[1]] , 'g' , label = 'v3')\n",
    "plt.plot([8,-8] , [0,0] , 'k--')\n",
    "plt.plot([0,0] , [8,-8] , 'k--')\n",
    "plt.grid()\n",
    "plt.axis((-8, 8, -8, 8))\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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fw/z75quoywlU2EWi2Kefws03Q1xc+DNKO3SAjTs3kpKRwoEjB1gwYAEt6xe/dYicX1TYRaLUa6/B7bdD48awbBk0bQrrdqwjKTWJAlfAwgELSbw4MeiYEoU0xy4SMWnSJJYuXRp0DI4ehd/8BsaMgW7d4P33oVo1WL19NR0mdSDugjjGJo6lab2mQUeVKKURu0hEw4YNqVevXqAZ9u+Hnj3DRf3hh+HPfw4X9ZU5K2n7TlviK8azaOAiLqsa/evtJTgq7CIRU6ZMYcGCBYGdf8cOaNcuXMz/8Af44x/DWwUsy15G+3fbUyO+BosHLubK2lcGllHKBxV2kYjXX3+dTz75JJBzb9wYXvmyZg189BGkpIAZfLntSzpO6kidqnVYNHARjWqV7BOB5PymOXaRgC1aBHfeGV75kp4O114b/v7CrQvp+kFXGl7YkPn3zefSCy8NNKeUHxqxiwTovfegY0e46KLwypfCoj53y1w6v9+Zy2teTvrAdBV1OSsq7CIBcA5GjoR+/eCGG8IbeRV+7vKnmZ/S7YNuNK7dmPQB6Vxc7eJgw0q5o6kYkTJ2+DAMGgRvvw39+8Nbb0GlSuG2jzd+TK+pvbjmomuY238u/1HlP4INK+WSCrtIxLRp0/jqq69K9RyhEPToAfPnwzPPhL/Mwm1T10+l7/S+tKzfktn3zqZmfM1SzSKxS4VdJKJOnTrUqFGj1Pr/9tvwRl6ZmZCaGv7g6ULvrXmP+z6+j9YNW/Np30+5sPKFpZZDYp/nOXYza2hmC81sg5mtN7NH/AgmUtZSU1OZM2dOqfS9YkV4OWN2NsyZc2JRT81Ipf+f+9Pmx22Yfe9sFXXxzI8XT48AjznnfgZcDzxkZlf50K9ImSqtwj5j+mHatIHKlcMvkrY7bsv08SvHc/9f7qfDFR2Y2Xcm1SpV8/38cv7xXNidc98751ZF/r0P2ABobZYI8NYvl3DH3RfQJOEQy5bBVccNeV7966sMmjmILld24ZN7PqFqXNXggkpMMeecf52ZXQ4sBpo65/ae1JYMJAPUrVu3RTR/Uk2hvLw8qlWL/hGUcvojJSWFgoICxo0b50t/P9qyhQMPTmJstWEMmlyJyj+yY21pWWm8/s3r3Fj7Rv7nqv8h7oK4s+o72h/LQsrpr7Zt2650zhW/T7NzzpcvoBqwEriruGMTEhJcebBw4cKgI5SIcvqjTZs2rlmzZv50Fgo599OfOnfJJc5t335C0/OLn3f8Ftczrac7dOTQOXUf7Y9lIeX0F7DClaAe+7IqxszigI+A95xz0/3oU6Tccg5++UvYuhUWLgy/rZTwIOrZRc/y7KJnuffqe0m9I5WKF2hhmvjP81VlZgZMADY4537vPZJIMGbNmsXixYu9d/T738P06TB6NNx0ExAu6k8teIoXvnyBgYkDeavbW1S4oIL3c4kUwY9VMTcA/YF2ZpYR+ersQ78iZapq1arEx8d76+SLL+CJJ+Cuu+DRR4FwUX987uO88OULDGoxiAm3T1BRl1LlecTunPsSsGIPFIlyr732GpmZmSQlJZ1bB9u3Q+/e4U1fJk4EM466ozwy+xFe/fpVhl47lFc6vYKZfl2kdGmCTyQiLS2NUCh0bnc+cgTuuSe8Z8CcOVCjBkfdUQbPHMz4VeN5rNVjvNzxZRV1KRMq7CJ+GDEivJl6aipccw0FRwv4rxn/RWpGKsNvHM7IdiNV1KXMqLCLePXJJ/Dii/DAAzBgAEeOHmHAxwN4f+37PJv0LCNuHqGiLmVKhV3Ei2++gfvug5//HP74Rw4XHObe6fcy9e9TGdVuFMNuGhZ0QjkPqbCLnKsDB+Duu8P77k6bxsGKRu+pPfnLpr8w5pYxPNrq0aATynlKhV0kIj09nfT09JLfYehQyMiAGTPIb3gJd6fdxax/zGLcbeN4+NqHSy2nSHFU2EXOxdtvw4QJMGwY+29txx0f3M68b+bxZtc3SW6RHHQ6Oc/pM09FIkaPHs2UKVOKPzAjA4YMgbZtyXv6N3R5vwvzvpnHxO4TVdQlKmjELhIxc+bM4texF362Xa1a7H1nPJ0/7MrS7KVMvmsyfa/uWzZBRYqhwi5SUs7B/ffDt98S+nwGnT7rx8rvV/Lh3R/Ss0nPoNOJHKPCLlJSo0fDxx+ze8xz3JL5NGt+WMO0ntPo/p/dg04mcgIVdpGSWLwYhg0jt3c3OlSdyqYdm/i4z8d0vlL73Un0UWEXiahSpQoHDhw4teH776F3b7Y3+THtb/gHW3d9y4x7ZtDxJx3LPqRICaiwi0TMnj371HXsR45Anz58VxCi3X2V+W5fFrPunUXS5UlBRBQpES13FDmTp55i2+rFtHnkQr4/tJs5/eaoqEvU04hdJOK5555j69at/96P/eOP2Tr+d7QbWp1/VTjI5/0+57oG1wWaUaQkVNhFIubPn//vdeybN/OPR/rRblAc+6vFMb//XFrUbxFsQJESUmEXOdmBA2y4vyvte+3ncM1aLBiwgGYXNws6lUiJ+TLHbmadzGyTmW02syf96FMkKOtS+pJ0/SaO1qxB+i8Xq6hLueN5xG5mFYD/BToC2cDXZvaJc+7vXvsWKWtHdm8nqeZqKlepxoJBy2hcp3HQkUTOmh9TMdcCm51z3wCY2YdAd+C0hT0rK4udO3dSp04dUlNTSU1NPeWYWbNmUbVqVV577TXS0tJOaS9cljZ69Ghmzpx5QluVKlWYPXs2EH5BbP78+Se0165dm48++giAYcOGsXTp0hPaGzRowOTJkwFISUkhIyPjhPaEhATGjx8PQHJyMpmZmSe0JyYmMnbsWAD69etHdnb2Ce2tWrXihRdeAODuu+9m165dJ7S3b9+eESNGAHDbbbedsra6a9euPP744wAkJSURCoWoWbPmsfZevXoxZMgQ9u/fT+fOp76BZuDAgQwcOJCdO3fSo0ePU9oHDx5M7969ycrKon///qe0P/bYY3Tr1o1NmzYxaNCgU9qffvppOnToQEZGBikpKce+X5hz1KhRtG7dmiVLljB8+PBT7j927FgSExOZN28eI0eOPKX9zTffpHHjxsyYMYMxY8ac0j5p0iQaNmzIlClTeP31109pnzZtWpHX3uqMlew5lEf9gkqkP7SCuWnzGZR26v9P196/r72TnXztnXxtBnXtFTrdtVeYM6hrr1Bxda+k/CjslwJZx93OBk5ZOmBmyUAyQFxcHF999RU1atRg48aNRW68tHjxYuLj48nMzCyyvfCXa8uWLae0Hzhw4Fj71q1bT2k/evTosfZt27ad0h4XF0d6ejp5eXlkZ2ef0p6Tk3Ps/jk5Oae0Z2dnH2v/4YcfTmnftm3bsfbc3Fz27t17QvvWrVuPte/evZuDBw+e0L5ly5Zj7aFQiIKCghPOkZmZSXp6Ovn5+UU+dhs3biQ9PZ09e/YU2b5+/XrS09PZsWNHke1r166levXqRT52AKtXr6ZixYps3rz5hPbCnKtWreLQoUOsW7euyPuvWLGCUCjE6tWri2xfvnw533//PWvXri2yfenSpWzZsoX169cX2X66a69OzSocPJLHS9eMJnv994Fee8AZr728vLyouPZOdvK1d/K1GdS1V+h0115hzqCuvULF1b0Sc855+gJ6Am8dd7s/MO5M90lISHDlwcKFC4OOUCLK6Z/PP5sVdIQSKQ+PpXPK6TdghStBXfbjxdNsoOFxtxsAOT70K1Kmhg0bxtvvTA46hohnfkzFfA1caWaNgO+APoA2ppZyZ+nSpd6e/opECc+F3Tl3xMweBj4DKgATnXPrPScTEZFz4ssblJxzs4BZfvQlIiLeaBMwEZEYoy0FRCIaNGhAXFxc0DFEPFNhF4mYPHnyqfuxi5RDmooREYkxGrGLRKSkpJCdnV3kW+VFyhMVdpGIjIwMrWOXmKCpGBGRGKPCLiISY1TYRURijObYRSISEhLIydH+dVL+qbCLRIwfP17r2CUmaCpGRCTGaMQuEpGcnExOTo7WsUu5p8IuEuH548hEooSmYkREYowKu4hIjFFhFxGJMZpjF4lITEwkOzs76Bginnkq7Gb2MtANOARsAe53zunVJymXxo4dq3XsEhO8TsV8DjR1zl0DZALDvEcSEREvPI3YnXNzj7u5DOjhLY5IcPr168cPP/ygdexS7plzzp+OzGYAU5xzk0/TngwkA9StW7dFWlqaL+ctTXl5eVSrVi3oGMVSTn+kpKRQUFDAuHHjgo5SrGh/LAspp7/atm270jnXsrjjii3sZjYPuLiIpqecc3+JHPMU0BK4y5XgL0Xjxo3dpk2bijsscOnp6eVi9Kac/khKSiIUCpGRkRF0lGJF+2NZSDn9ZWYlKuzFTsU45zoUc6IBQFegfUmKuoiIlC6vq2I6AU8AbZxz+/2JJCIiXnhdx/4qUBn43MwAljnnHvScSiQArVq1Ytu2bUHHEPHM66qYn/oVRCRoL7zwgtaxS0zQlgIiIjFGWwqIRNx9993k5uayePHioKOIeKIRu0jErl272Lt3b9AxRDxTYRcRiTEq7CIiMUaFXUQkxujFU5GI9u3bs3Xr1qBjiHimwi4SMWLECK1jl5igqRgRkRijEbtIxG233cbu3btZvnx50FFEPNGIXSTiwIEDHDx4MOgYIp6psIuIxBgVdhGRGKPCLiISY/TiqUhE165d2bJlS9AxRDxTYReJePzxx7WOXWKCpmJERGKMRuwiEUlJSYRCITIyMoKOIuKJLyN2M3vczJyZ1fGjPxEROXeeC7uZNQQ6AvoUYBGRKODHiP0PwG8A50NfIiLikac5djO7HfjOObfazIo7NhlIBqhbt265WH2Ql5ennD6K9pyhUIiCgoKozlgo2h/LQsoZjGILu5nNAy4uoukpYDhwS0lO5JwbD4wHaNy4sUtKSip5yoCkp6ejnP6J9pzJyclkZmZGdcZC0f5YFlLOYBRb2J1zHYr6vpldDTQCCkfrDYBVZnatc267rylFysCQIUNiatQm569znopxzq0F6hXeNrN/Ai2dczt9yCVS5vbv309+fn7QMUQ80zp2kYjOnTsTCoXo1KlT0FFEPPGtsDvnLverLxEROXfaUkBEJMaosIuIxBgVdhGRGKMXT0UiBg4cyMaNG4OOIeKZCrtIxMCBA7WOXWKCpmJEInbu3MmePXuCjiHimUbsIhE9evQgFArRvXv3oKOIeKIRu4hIjFFhFxGJMSrsIiIxRoVdRCTG6MVTkYjBgwezfv36oGOIeKbCLhLRu3dvrWOXmKCpGJGIrKwsduzYEXQMEc80YheJ6N+/P6FQiF69egUdRcQTjdhFRGKMCruISIxRYRcRiTGeC7uZDTWzTWa23sx+50coERE5d55ePDWztkB34Brn3EEzq+dPLJGy99hjj7F27dqgY4h45nVVzGDgRefcQQDnnNaKSbnVrVs3qlevHnQMEc+8TsUkADeZ2XIzW2Rmv/AjlEgQNm3axLZt24KOIeKZOefOfIDZPODiIpqeAp4HFgCPAL8ApgBXuCI6NbNkIBmgbt26LdLS0rwlLwN5eXlUq1Yt6BjFUk5/pKSkUFBQwLhx44KOUqxofywLKae/2rZtu9I517LYA51z5/wFzAGSjru9Bahb3P0SEhJcebBw4cKgI5SIcvqjTZs2rlmzZkHHKJFofywLKae/gBWuBLXZ61TMx0A7ADNLACoBOz32KSIiHnh98XQiMNHM1gGHgAGRvyoiIhIQT4XdOXcI6OdTFhER8YE2AROJePrpp1m9enXQMUQ8U2EXiejQoQMVK+pXQso/7RUjEpGRkcHmzZuDjiHimQq7SERKSgqvvvpq0DFEPFNhFxGJMSrsIiIxRoVdRCTGqLCLiMQYre0SiRg1ahSrVq0KOoaIZyrsIhGtW7fm0KFDQccQ8UxTMSIRS5YsYd26dUHHEPFMhV0kYvjw4bz11ltBxxDxTIVdRCTGqLCLiMQYFXYRkRijwi4iEmO03FEkYuzYsaxYsSLoGCKeqbCLRCQmJhIKhYKOIeKZpmJEIubNm8fKlSuDjiHimafCbmaJZrbMzDLMbIWZXetXMJGyNnLkSCZNmhR0DBHPvI7Yfwc865xLBP4ncltERALktbA74MLIv2sAOR77ExERj8w5d+53Nvtx954aAAAEuUlEQVQZ8BlghP9ItHbOfXuaY5OB5MjNpkB52JSjDrAz6BAloJz+KQ8ZQTn9Vl5yNnbOVS/uoGILu5nNAy4uoukpoD2wyDn3kZn1ApKdcx2KPanZCudcy+KOC5py+qs85CwPGUE5/RZrOYtd7nimQm1m7wKPRG5OBbSDkohIwLzOsecAbSL/bgf8w2N/IiLikdc3KD0AvGJmFYF8/j2HXpzxHs9bVpTTX+UhZ3nICMrpt5jK6enFUxERiT5656mISIxRYRcRiTGBFfbytB2BmQ01s01mtt7MovbdtWb2uJk5M6sTdJaimNnLZrbRzNaY2Z/NrGbQmY5nZp0iP+fNZvZk0HmKYmYNzWyhmW2IXI+PFH+vYJhZBTP7m5nNDDrL6ZhZTTObFrkuN5hZq6AzFcXMfhX5ea8zsw/MLP5Mxwc5Yi8X2xGYWVugO3CNc64JMDrgSEUys4ZAR2Bb0FnO4HOgqXPuGiATGBZwnmPMrALwv8BtwFXAPWZ2VbCpinQEeMw59zPgeuChKM0J4aXQG4IOUYxXgDnOuf8EmhGFec3sUuC/gZbOuaZABaDPme4TZGEvL9sRDAZedM4dBHDO7Qg4z+n8AfgN4cc1Kjnn5jrnjkRuLgMaBJnnJNcCm51z3zjnDgEfEv6DHlWcc98751ZF/r2PcCG6NNhUpzKzBkAXovi9LWZ2IXAzMAHAOXfIORet+zZXBKpEViBWpZh6GWRhTwFeNrMswqPgqBm9nSQBuMnMlpvZIjP7RdCBTmZmtwPfOedWB53lLPwSmB10iONcCmQddzubKCyYxzOzy4HmwPJgkxRpLOGBxtGgg5zBFUAu8HZkyugtM/tR0KFO5pz7jnCN3AZ8D+xxzs09031K9YM2SrAdwa+O245gAlDsdgSloZicFYFahJ/2/gJIM7MrXBmvEy0m43DglrLMczpnyumc+0vkmKcITym8V5bZimFFfC9qn/2YWTXgIyDFObc36DzHM7OuwA7n3EozSwo6zxlUBH4ODHXOLTezV4AngRHBxjqRmdUi/OyxERACpppZP+fc5NPdp1QLe3nZjqCYnIOB6ZFC/lczO0p4w6DcssoHp89oZlcT/oGvNjMIT2+sMrNrnXPbyzAicObHEsDMBgBdgfZl/cexGNlAw+NuNyBKpwfNLI5wUX/POTc96DxFuAG43cw6A/HAhWY22TnXL+BcJ8sGsp1zhc94phEu7NGmA7DVOZcLYGbTgdbAaQt7kFMx5WU7go8J58PMEoBKRNEucM65tc65es65y51zlxO+WH8eRFEvjpl1Ap4AbnfO7Q86z0m+Bq40s0ZmVonwi1OfBJzpFBb+6z0B2OCc+33QeYrinBvmnGsQuR77AAuisKgT+R3JMrPGkW+1B/4eYKTT2QZcb2ZVIz//9hTzIm+Qn3l6rtsRlLWJwEQzWwccAgZE2UizPHkVqAx8Hnl2scw592CwkcKcc0fM7GHC21BXACY659YHHKsoNwD9gbVmlhH53nDn3KwAM5VnQ4H3In/MvwHuDzjPKSLTRNOAVYSnMP9GMVsLaEsBEZEYo3eeiojEGBV2EZEYo8IuIhJjVNhFRGKMCruISIxRYRcRiTEq7CIiMeb/AGGMQWB60KOrAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot([0,v1[0]] , [0,v1[1]] , 'r' , label = 'v1')\n",
    "plt.plot([0,v2[0]]+v1[0] , [0,v2[1]]+v1[1], 'b' , label = 'v2')\n",
    "plt.plot([0,v3[0]] , [0,v3[1]] , 'g' , label = 'v3')\n",
    "plt.plot([8,-8] , [0,0] , 'k--')\n",
    "plt.plot([0,0] , [8,-8] , 'k--')\n",
    "plt.grid()\n",
    "plt.axis((-8, 8, -8, 8))\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Scalar Multiplication"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "u1 = np.array([3,4])\n",
    "a = .5\n",
    "u2 = u1*a\n",
    "plt.plot([0,u1[0]] , [0,u1[1]] , 'r' , label = 'v1')\n",
    "plt.plot([0,u2[0]] , [0,u2[1]], 'b--' , label = 'v2')\n",
    "plt.plot([8,-8] , [0,0] , 'k--')\n",
    "plt.plot([0,0] , [8,-8] , 'k--')\n",
    "plt.grid()\n",
    "plt.axis((-8, 8, -8, 8))\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "u1 = np.array([3,4])\n",
    "a = -.3\n",
    "u2 = u1*a\n",
    "plt.plot([0,u1[0]] , [0,u1[1]] , 'r' , label = 'v1')\n",
    "plt.plot([0,u2[0]] , [0,u2[1]], 'b' , label = 'v2')\n",
    "plt.plot([8,-8] , [0,0] , 'k--')\n",
    "plt.plot([0,0] , [8,-8] , 'k--')\n",
    "plt.grid()\n",
    "plt.axis((-8, 8, -8, 8))\n",
    "plt.legend()\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Multiplication of vectors"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[20 42 72]\n"
     ]
    }
   ],
   "source": [
    "a1 = [5 , 6 ,8]\n",
    "a2 = [4, 7 , 9]\n",
    "print(np.multiply(a1,a2))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Dot Product"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Dot Product :\n",
    "- https://www.youtube.com/watch?v=WNuIhXo39_k\n",
    "- https://www.youtube.com/watch?v=LyGKycYT2v0"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      " Dot product -  32\n",
      " Dot product usign np.dot 32\n",
      " Dot product usign np.inner 32\n",
      " Dot product usign np.multiply & sum 32\n",
      " Dot product usign np.matmul 32\n",
      " Dot product usign for loop 32\n"
     ]
    }
   ],
   "source": [
    "a1 = np.array([1,2,3])\n",
    "a2 = np.array([4,5,6])\n",
    "\n",
    "dotp = a1@a2\n",
    "print(\" Dot product - \",dotp)\n",
    "\n",
    "dotp = np.dot(a1,a2)\n",
    "print(\" Dot product usign np.dot\",dotp)\n",
    "\n",
    "dotp = np.inner(a1,a2)\n",
    "print(\" Dot product usign np.inner\", dotp)\n",
    "\n",
    "dotp = sum(np.multiply(a1,a2))\n",
    "print(\" Dot product usign np.multiply & sum\",dotp)\n",
    "\n",
    "dotp = np.matmul(a1,a2)\n",
    "print(\" Dot product usign np.matmul\",dotp)\n",
    "\n",
    "dotp = 0\n",
    "for i in range(len(a1)):\n",
    "    dotp = dotp + a1[i]*a2[i]\n",
    "print(\" Dot product usign for loop\" , dotp)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Length of Vector"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "9.539392014169456"
      ]
     },
     "execution_count": 43,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "v3 = np.array([1,2,3,4,5,6])\n",
    "length = np.sqrt(np.dot(v3,v3))\n",
    "length"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "9.539392014169456"
      ]
     },
     "execution_count": 44,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "v3 = np.array([1,2,3,4,5,6])\n",
    "length = np.sqrt(sum(np.multiply(v3,v3)))\n",
    "length"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "9.539392014169456"
      ]
     },
     "execution_count": 45,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "v3 = np.array([1,2,3,4,5,6])\n",
    "length = np.sqrt(np.matmul(v3,v3))\n",
    "length"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Normalized Vector"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "How to normalize a vector : https://www.youtube.com/watch?v=7fn03DIW3Ak"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(3.605551275463989, array([0.5547002 , 0.83205029]))"
      ]
     },
     "execution_count": 46,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "v1 = [2,3]\n",
    "length_v1 = np.sqrt(np.dot(v1,v1))\n",
    "norm_v1 = v1/length_v1\n",
    "length_v1 , norm_v1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0.5547002 , 0.83205029])"
      ]
     },
     "execution_count": 47,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "v1 = [2,3]\n",
    "norm_v1 = v1/np.linalg.norm(v1)\n",
    "norm_v1"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Angle between vectors"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Angle between two vectors : https://www.youtube.com/watch?v=WDdR5s0C4cY"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "#First Method\n",
    "v1 = np.array([8,4])\n",
    "v2 = np.array([-4,8])\n",
    "ang = np.rad2deg(np.arccos( np.dot(v1,v2) / (np.linalg.norm(v1)*np.linalg.norm(v2))))\n",
    "plt.plot([0,v1[0]] , [0,v1[1]] , 'r' , label = 'v1')\n",
    "plt.plot([0,v2[0]]+v1[0] , [0,v2[1]]+v1[1], 'b' , label = 'v2')\n",
    "plt.plot([16,-16] , [0,0] , 'k--')\n",
    "plt.plot([0,0] , [16,-16] , 'k--')\n",
    "plt.grid()\n",
    "plt.axis((-16, 16, -16, 16))\n",
    "plt.legend()\n",
    "plt.title('Angle between Vectors - %s'  %ang)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Angle between Vectors - 90.0\n"
     ]
    }
   ],
   "source": [
    "#Second Method\n",
    "v1 = np.array([4,3])\n",
    "v2 = np.array([-3,4])\n",
    "lengthV1 = np.sqrt(np.dot(v1,v1)) \n",
    "lengthV2  = np.sqrt(np.dot(v2,v2))\n",
    "ang = np.rad2deg(np.arccos( np.dot(v1,v2) / (lengthV1 * lengthV2)))\n",
    "print('Angle between Vectors - %s' %ang)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5,0.92,'Angle between vectors: 103.01589221967097 degrees.')"
      ]
     },
     "execution_count": 50,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "v1 = np.array([1,2,-3])\n",
    "v2 = np.array([7,-4,2])\n",
    "fig = plt.figure()\n",
    "ax = Axes3D(fig)\n",
    "ax.plot([0, v1[0]],[0, v1[1]],[0, v1[2]],'b')\n",
    "ax.plot([0, v2[0]],[0, v2[1]],[0, v2[2]],'r')\n",
    "ang = np.rad2deg(np.arccos( np.dot(v1,v2) / (np.linalg.norm(v1)*np.linalg.norm(v2)) ))\n",
    "plt.title('Angle between vectors: %s degrees.' %ang)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Inner & outer products"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Inner and Outer Product : https://www.youtube.com/watch?v=FCmH4MqbFGs&t=2s"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      " Inner Product ==>  \n",
      " 32\n",
      "\n",
      " Outer Product ==>  \n",
      " [[ 4  5  6]\n",
      " [ 8 10 12]\n",
      " [12 15 18]]\n"
     ]
    }
   ],
   "source": [
    "# https://www.youtube.com/watch?v=FCmH4MqbFGs\n",
    "\n",
    "v1 = np.array([1,2,3])\n",
    "v2 = np.array([4,5,6])\n",
    "np.inner(v1,v2)\n",
    "\n",
    "print(\"\\n Inner Product ==>  \\n\", np.inner(v1,v2))\n",
    "print(\"\\n Outer Product ==>  \\n\", np.outer(v1,v2))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Vector Cross Product"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Vector Cross Product : https://www.youtube.com/watch?v=pWbOisq1MJU"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "Vector Cross Product ==>  \n",
      " [-3  6 -3]\n"
     ]
    }
   ],
   "source": [
    "v1 = np.array([1,2,3])\n",
    "v2 = np.array([4,5,6])\n",
    "print(\"\\nVector Cross Product ==>  \\n\", np.cross(v1,v2))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Matrix Operations"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "##  Matrix Creation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {},
   "outputs": [],
   "source": [
    "A = np.array([[1,2,3,4] , [5,6,7,8] , [10 , 11 , 12 ,13] , [14,15,16,17]])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 1,  2,  3,  4],\n",
       "       [ 5,  6,  7,  8],\n",
       "       [10, 11, 12, 13],\n",
       "       [14, 15, 16, 17]])"
      ]
     },
     "execution_count": 54,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "A"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "numpy.ndarray"
      ]
     },
     "execution_count": 55,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "type(A)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "dtype('int32')"
      ]
     },
     "execution_count": 56,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "A.dtype"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 57,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 1.5 ,  2.07,  3.  ,  4.  ],\n",
       "       [ 5.  ,  6.  ,  7.  ,  8.  ],\n",
       "       [10.  , 11.  , 12.  , 13.  ],\n",
       "       [14.  , 15.  , 16.  , 17.  ]])"
      ]
     },
     "execution_count": 57,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "B = np.array([[1.5,2.07,3,4] , [5,6,7,8] , [10 , 11 , 12 ,13] , [14,15,16,17]])\n",
    "B"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 58,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "numpy.ndarray"
      ]
     },
     "execution_count": 58,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "type(B)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 59,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "dtype('float64')"
      ]
     },
     "execution_count": 59,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "B.dtype"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 60,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(4, 4)"
      ]
     },
     "execution_count": 60,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "A.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([1, 2, 3, 4])"
      ]
     },
     "execution_count": 61,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "A[0,]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 1,  5, 10, 14])"
      ]
     },
     "execution_count": 62,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "A[:,0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 63,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1"
      ]
     },
     "execution_count": 63,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "A[0,0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 64,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1"
      ]
     },
     "execution_count": 64,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "A[0][0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 65,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 6,  7],\n",
       "       [11, 12]])"
      ]
     },
     "execution_count": 65,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "A[1:3 , 1:3]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Matrix Types : \n",
    "   - https://www.youtube.com/watch?v=alc9i7V2e9Q&list=PLmdFyQYShrjcoVkhCCIwxNj9N4rW1-T5I&index=5\n",
    "   - https://www.youtube.com/watch?v=nfG4NwLhH14&list=PLmdFyQYShrjcoVkhCCIwxNj9N4rW1-T5I&index=6"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Zero Matrix"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Zero Matrix - https://www.web-formulas.com/Math_Formulas/Linear_Algebra_Definition_of_Zero_Matrix.aspx"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[0., 0., 0.],\n",
       "       [0., 0., 0.],\n",
       "       [0., 0., 0.]])"
      ]
     },
     "execution_count": 66,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.zeros(9).reshape(3,3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 67,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[0., 0., 0.],\n",
       "       [0., 0., 0.],\n",
       "       [0., 0., 0.]])"
      ]
     },
     "execution_count": 67,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.zeros((3,3))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Matrix of Ones"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Matrix of Ones - https://en.wikipedia.org/wiki/Matrix_of_ones"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 68,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1., 1., 1.],\n",
       "       [1., 1., 1.],\n",
       "       [1., 1., 1.]])"
      ]
     },
     "execution_count": 68,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.ones(9).reshape(3,3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 69,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1., 1., 1.],\n",
       "       [1., 1., 1.],\n",
       "       [1., 1., 1.]])"
      ]
     },
     "execution_count": 69,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.ones((3,3))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Matrix with Random Numbers"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 70,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[0.30088476, 0.83059469, 0.44002496],\n",
       "       [0.36264188, 0.14854413, 0.28324881],\n",
       "       [0.37934998, 0.30606346, 0.02852849]])"
      ]
     },
     "execution_count": 70,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "X = np.random.random((3,3))\n",
    "X"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Identity Matrix"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Identity Matrix : https://en.wikipedia.org/wiki/Identity_matrix"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 71,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1., 0., 0., 0., 0., 0., 0., 0., 0.],\n",
       "       [0., 1., 0., 0., 0., 0., 0., 0., 0.],\n",
       "       [0., 0., 1., 0., 0., 0., 0., 0., 0.],\n",
       "       [0., 0., 0., 1., 0., 0., 0., 0., 0.],\n",
       "       [0., 0., 0., 0., 1., 0., 0., 0., 0.],\n",
       "       [0., 0., 0., 0., 0., 1., 0., 0., 0.],\n",
       "       [0., 0., 0., 0., 0., 0., 1., 0., 0.],\n",
       "       [0., 0., 0., 0., 0., 0., 0., 1., 0.],\n",
       "       [0., 0., 0., 0., 0., 0., 0., 0., 1.]])"
      ]
     },
     "execution_count": 71,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "I = np.eye(9)\n",
    "I"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Diagonal Matrix "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Diagonal Matrix : https://en.wikipedia.org/wiki/Diagonal_matrix"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 72,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1, 0, 0, 0, 0, 0, 0, 0],\n",
       "       [0, 2, 0, 0, 0, 0, 0, 0],\n",
       "       [0, 0, 3, 0, 0, 0, 0, 0],\n",
       "       [0, 0, 0, 4, 0, 0, 0, 0],\n",
       "       [0, 0, 0, 0, 5, 0, 0, 0],\n",
       "       [0, 0, 0, 0, 0, 6, 0, 0],\n",
       "       [0, 0, 0, 0, 0, 0, 7, 0],\n",
       "       [0, 0, 0, 0, 0, 0, 0, 8]])"
      ]
     },
     "execution_count": 72,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "D = np.diag([1,2,3,4,5,6,7,8])\n",
    "D"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Traingular Matrices (lower & Upper triangular matrix)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Traingular Matrices : https://en.wikipedia.org/wiki/Triangular_matrix"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 85,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "lower triangular matrix - \n",
      " [[ 0.04163482  0.84694284  1.27184552  0.49068035  1.89525349]\n",
      " [ 0.2935111  -0.38527099 -0.36726567  0.05388857 -0.03050685]\n",
      " [ 1.02687751 -1.0205883  -0.05963054  1.86996511 -0.48568312]\n",
      " [-1.17758131  1.08224614  0.62710458 -0.23134112  0.36333312]\n",
      " [-1.8826224  -0.70551637  0.09074075  1.10122071 -0.07975198]]\n",
      "\n",
      "\n",
      "lower triangular matrix - \n",
      " [[ 0.04163482  0.          0.          0.          0.        ]\n",
      " [ 0.2935111  -0.38527099  0.          0.          0.        ]\n",
      " [ 1.02687751 -1.0205883  -0.05963054  0.          0.        ]\n",
      " [-1.17758131  1.08224614  0.62710458 -0.23134112  0.        ]\n",
      " [-1.8826224  -0.70551637  0.09074075  1.10122071 -0.07975198]]\n",
      "\n",
      "\n",
      "Upper triangular matrix - \n",
      " [[ 0.04163482  0.84694284  1.27184552  0.49068035  1.89525349]\n",
      " [ 0.         -0.38527099 -0.36726567  0.05388857 -0.03050685]\n",
      " [ 0.          0.         -0.05963054  1.86996511 -0.48568312]\n",
      " [ 0.          0.          0.         -0.23134112  0.36333312]\n",
      " [ 0.          0.          0.          0.         -0.07975198]]\n"
     ]
    }
   ],
   "source": [
    "M = np.random.randn(5,5)\n",
    "U = np.triu(M)\n",
    "L = np.tril(M)\n",
    "print(\"lower triangular matrix - \\n\" , M)\n",
    "print(\"\\n\")\n",
    "\n",
    "\n",
    "print(\"lower triangular matrix - \\n\" , L)\n",
    "print(\"\\n\")\n",
    "\n",
    "print(\"Upper triangular matrix - \\n\" , U)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Concatenate Matrices"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Matrix Concatenation : https://docs.scipy.org/doc/numpy/reference/generated/numpy.concatenate.html"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 599,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(array([[1, 2],\n",
       "        [3, 4],\n",
       "        [5, 6],\n",
       "        [1, 1],\n",
       "        [1, 1]]), (5, 2), numpy.ndarray, dtype('int32'))"
      ]
     },
     "execution_count": 599,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "A = np.array([[1,2] , [3,4] ,[5,6]])\n",
    "B = np.array([[1,1] , [1,1]])\n",
    "C = np.concatenate((A,B))\n",
    "C , C.shape , type(C) , C.dtype"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 486,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[8, 8, 8, 8, 8],\n",
       "       [8, 8, 8, 8, 8],\n",
       "       [8, 8, 8, 8, 8],\n",
       "       [8, 8, 8, 8, 8],\n",
       "       [8, 8, 8, 8, 8]])"
      ]
     },
     "execution_count": 486,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.full((5,5) , 8)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 490,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 1,  2,  3],\n",
       "       [ 4, -3,  6],\n",
       "       [ 7,  8,  0]])"
      ]
     },
     "execution_count": 490,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "M"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 491,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 1,  2,  3,  4, -3,  6,  7,  8,  0])"
      ]
     },
     "execution_count": 491,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "M.flatten()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Matrix Addition"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Matrix Addition : https://www.youtube.com/watch?v=ZCmVpGv6_1g"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 397,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      " First Matrix (M)  ==>  \n",
      " [[ 1  2  3]\n",
      " [ 4 -3  6]\n",
      " [ 7  8  0]]\n",
      "\n",
      " Second Matrix (N)  ==>  \n",
      " [[1 1 1]\n",
      " [2 2 2]\n",
      " [3 3 3]]\n",
      "\n",
      " Matrix Addition (M+N)  ==>  \n",
      " [[ 2  3  4]\n",
      " [ 6 -1  8]\n",
      " [10 11  3]]\n",
      "\n",
      " Matrix Addition using np.add  ==>  \n",
      " [[ 2.  3.  4.]\n",
      " [ 6. -1.  8.]\n",
      " [10. 11.  3.]]\n"
     ]
    }
   ],
   "source": [
    "#********************************************************#\n",
    "M = np.array([[1,2,3],[4,-3,6],[7,8,0]])\n",
    "N = np.array([[1,1,1],[2,2,2],[3,3,3]])\n",
    "\n",
    "print(\"\\n First Matrix (M)  ==>  \\n\", M)\n",
    "print(\"\\n Second Matrix (N)  ==>  \\n\", N)\n",
    "\n",
    "C = M+N\n",
    "print(\"\\n Matrix Addition (M+N)  ==>  \\n\", C)\n",
    "\n",
    "# OR\n",
    "\n",
    "C = np.add(M,N,dtype = np.float64)\n",
    "print(\"\\n Matrix Addition using np.add  ==>  \\n\", C)\n",
    "\n",
    "#********************************************************#"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Matrix subtraction"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Matrix subtraction : https://www.youtube.com/watch?v=7jb_AO_hRc8&list=PLmdFyQYShrjcoVkhCCIwxNj9N4rW1-T5I&index=8"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 398,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      " First Matrix (M)  ==>  \n",
      " [[ 1  2  3]\n",
      " [ 4 -3  6]\n",
      " [ 7  8  0]]\n",
      "\n",
      " Second Matrix (N)  ==>  \n",
      " [[1 1 1]\n",
      " [2 2 2]\n",
      " [3 3 3]]\n",
      "\n",
      " Matrix Subtraction (M-N)  ==>  \n",
      " [[ 0  1  2]\n",
      " [ 2 -5  4]\n",
      " [ 4  5 -3]]\n",
      "\n",
      " Matrix Subtraction using np.subtract  ==>  \n",
      " [[ 0.  1.  2.]\n",
      " [ 2. -5.  4.]\n",
      " [ 4.  5. -3.]]\n"
     ]
    }
   ],
   "source": [
    "#********************************************************#\n",
    "M = np.array([[1,2,3],[4,-3,6],[7,8,0]])\n",
    "N = np.array([[1,1,1],[2,2,2],[3,3,3]])\n",
    "\n",
    "print(\"\\n First Matrix (M)  ==>  \\n\", M)\n",
    "print(\"\\n Second Matrix (N)  ==>  \\n\", N)\n",
    "\n",
    "C = M-N\n",
    "print(\"\\n Matrix Subtraction (M-N)  ==>  \\n\", C)\n",
    "\n",
    "# OR\n",
    "\n",
    "C = np.subtract(M,N,dtype = np.float64)\n",
    "print(\"\\n Matrix Subtraction using np.subtract  ==>  \\n\", C)\n",
    "\n",
    "#********************************************************#"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Matrices Scalar Multiplication"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Matrices Scalar Multiplication : https://www.youtube.com/watch?v=4lHyTQH1iS8&list=PLmdFyQYShrjcoVkhCCIwxNj9N4rW1-T5I&index=9"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 90,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      " Matrix (M)  ==>  \n",
      " [[ 1  2  3]\n",
      " [ 4 -3  6]\n",
      " [ 7  8  0]]\n",
      "\n",
      "Matrices Scalar Multiplication ==>  \n",
      " [[ 10  20  30]\n",
      " [ 40 -30  60]\n",
      " [ 70  80   0]]\n",
      "\n",
      "Matrices Scalar Multiplication ==>  \n",
      " [[ 10  20  30]\n",
      " [ 40 -30  60]\n",
      " [ 70  80   0]]\n"
     ]
    }
   ],
   "source": [
    "M = np.array([[1,2,3],[4,-3,6],[7,8,0]])\n",
    "\n",
    "C = 10\n",
    "\n",
    "print(\"\\n Matrix (M)  ==>  \\n\", M)\n",
    "\n",
    "print(\"\\nMatrices Scalar Multiplication ==>  \\n\", C*M)\n",
    "\n",
    "# OR\n",
    "\n",
    "print(\"\\nMatrices Scalar Multiplication ==>  \\n\", np.multiply(C,M))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Transpose of a matrix"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Transpose of a matrix : https://www.youtube.com/watch?v=g_Rz94DXvNo&list=PLmdFyQYShrjcoVkhCCIwxNj9N4rW1-T5I&index=13"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 425,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      " Matrix (M)  ==>  \n",
      " [[ 1  2  3]\n",
      " [ 4 -3  6]\n",
      " [ 7  8  0]]\n",
      "\n",
      "Transpose of M ==>  \n",
      " [[ 1  4  7]\n",
      " [ 2 -3  8]\n",
      " [ 3  6  0]]\n",
      "\n",
      "Transpose of M ==>  \n",
      " [[ 1  4  7]\n",
      " [ 2 -3  8]\n",
      " [ 3  6  0]]\n"
     ]
    }
   ],
   "source": [
    "M = np.array([[1,2,3],[4,-3,6],[7,8,0]])\n",
    "\n",
    "print(\"\\n Matrix (M)  ==>  \\n\", M)\n",
    "\n",
    "print(\"\\nTranspose of M ==>  \\n\", np.transpose(M))\n",
    "\n",
    "# OR\n",
    "\n",
    "print(\"\\nTranspose of M ==>  \\n\", M.T)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Determinant of a matrix"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Determinant of a matrix : \n",
    "- https://www.youtube.com/watch?v=21LWuY8i6Hw&t=88s\n",
    "- https://www.youtube.com/watch?v=Ip3X9LOh2dk&list=PLZHQObOWTQDPD3MizzM2xVFitgF8hE_ab&index=6"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 404,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      " Matrix (M)  ==>  \n",
      " [[ 1  2  3]\n",
      " [ 4 -3  6]\n",
      " [ 7  8  0]]\n",
      "\n",
      "Determinant of M ==>   195.0\n"
     ]
    }
   ],
   "source": [
    "M = np.array([[1,2,3],[4,-3,6],[7,8,0]])\n",
    "\n",
    "print(\"\\n Matrix (M)  ==>  \\n\", M)\n",
    "\n",
    "print(\"\\nDeterminant of M ==>  \", np.linalg.det(M))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Rank of a matrix"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 405,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      " Matrix (M)  ==>  \n",
      " [[ 1  2  3]\n",
      " [ 4 -3  6]\n",
      " [ 7  8  0]]\n",
      "\n",
      "Rank of M ==>  3\n"
     ]
    }
   ],
   "source": [
    "M = np.array([[1,2,3],[4,-3,6],[7,8,0]])\n",
    "\n",
    "print(\"\\n Matrix (M)  ==>  \\n\", M)\n",
    "\n",
    "print(\"\\nRank of M ==> \", np.linalg.matrix_rank(M))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Trace of matrix"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 602,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      " Matrix (M)  ==>  \n",
      " [[ 1  2  3]\n",
      " [ 4 -3  6]\n",
      " [ 7  8  0]]\n",
      "\n",
      "Trace of M ==>  -2\n"
     ]
    }
   ],
   "source": [
    "M = np.array([[1,2,3],[4,-3,6],[7,8,0]])\n",
    "\n",
    "print(\"\\n Matrix (M)  ==>  \\n\", M)\n",
    "\n",
    "print(\"\\nTrace of M ==> \", np.trace(M))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Inverse of matrix A"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Inverse of matrix : https://www.youtube.com/watch?v=pKZyszzmyeQ"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 407,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      " Matrix (M)  ==>  \n",
      " [[ 1  2  3]\n",
      " [ 4 -3  6]\n",
      " [ 7  8  0]]\n",
      "\n",
      "Inverse of M ==> \n",
      " [[-0.24615385  0.12307692  0.10769231]\n",
      " [ 0.21538462 -0.10769231  0.03076923]\n",
      " [ 0.27179487  0.03076923 -0.05641026]]\n"
     ]
    }
   ],
   "source": [
    "M = np.array([[1,2,3],[4,-3,6],[7,8,0]])\n",
    "\n",
    "print(\"\\n Matrix (M)  ==>  \\n\", M)\n",
    "\n",
    "print(\"\\nInverse of M ==> \\n\", np.linalg.inv(M))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Matrix Multiplication (pointwise multiplication)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 409,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      " First Matrix (M)  ==>  \n",
      " [[ 1  2  3]\n",
      " [ 4 -3  6]\n",
      " [ 7  8  0]]\n",
      "\n",
      " Second Matrix (N)  ==>  \n",
      " [[1 1 1]\n",
      " [2 2 2]\n",
      " [3 3 3]]\n",
      "\n",
      " Point-Wise Multiplication of M & N  ==> \n",
      " [[ 1  2  3]\n",
      " [ 8 -6 12]\n",
      " [21 24  0]]\n",
      "\n",
      " Point-Wise Multiplication of M & N  ==> \n",
      " [[ 1  2  3]\n",
      " [ 8 -6 12]\n",
      " [21 24  0]]\n"
     ]
    }
   ],
   "source": [
    "M = np.array([[1,2,3],[4,-3,6],[7,8,0]])\n",
    "N = np.array([[1,1,1],[2,2,2],[3,3,3]])\n",
    "\n",
    "print(\"\\n First Matrix (M)  ==>  \\n\", M)\n",
    "print(\"\\n Second Matrix (N)  ==>  \\n\", N)\n",
    "\n",
    "print(\"\\n Point-Wise Multiplication of M & N  ==> \\n\", M*N)\n",
    "\n",
    "# OR\n",
    "\n",
    "print(\"\\n Point-Wise Multiplication of M & N  ==> \\n\", np.multiply(M,N))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Matrix dot product"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Matrix Multiplication : \n",
    "- https://www.youtube.com/watch?v=vzt9c7iWPxs&t=207s\n",
    "- https://www.youtube.com/watch?v=XkY2DOUCWMU&list=PLZHQObOWTQDPD3MizzM2xVFitgF8hE_ab&index=4"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 411,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      " First Matrix (M)  ==>  \n",
      " [[ 1  2  3]\n",
      " [ 4 -3  6]\n",
      " [ 7  8  0]]\n",
      "\n",
      " Second Matrix (N)  ==>  \n",
      " [[1 1 1]\n",
      " [2 2 2]\n",
      " [3 3 3]]\n",
      "\n",
      " Matrix Dot Product ==> \n",
      " [[14 14 14]\n",
      " [16 16 16]\n",
      " [23 23 23]]\n",
      "\n",
      " Matrix Dot Product using np.matmul ==> \n",
      " [[14 14 14]\n",
      " [16 16 16]\n",
      " [23 23 23]]\n",
      "\n",
      " Matrix Dot Product using np.dot ==> \n",
      " [[14 14 14]\n",
      " [16 16 16]\n",
      " [23 23 23]]\n"
     ]
    }
   ],
   "source": [
    "M = np.array([[1,2,3],[4,-3,6],[7,8,0]])\n",
    "N = np.array([[1,1,1],[2,2,2],[3,3,3]])\n",
    "\n",
    "print(\"\\n First Matrix (M)  ==>  \\n\", M)\n",
    "print(\"\\n Second Matrix (N)  ==>  \\n\", N)\n",
    "\n",
    "print(\"\\n Matrix Dot Product ==> \\n\", M@N)\n",
    "\n",
    "# OR\n",
    "\n",
    "print(\"\\n Matrix Dot Product using np.matmul ==> \\n\", np.matmul(M,N))\n",
    "\n",
    "# OR\n",
    "\n",
    "print(\"\\n Matrix Dot Product using np.dot ==> \\n\", np.dot(M,N))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Matrix Division"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 413,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      " First Matrix (M)  ==>  \n",
      " [[ 1  2  3]\n",
      " [ 4 -3  6]\n",
      " [ 7  8  0]]\n",
      "\n",
      " Second Matrix (N)  ==>  \n",
      " [[1 1 1]\n",
      " [2 2 2]\n",
      " [3 3 3]]\n",
      "\n",
      " Matrix Division (M/N)   ==> \n",
      " [[ 1.          2.          3.        ]\n",
      " [ 2.         -1.5         3.        ]\n",
      " [ 2.33333333  2.66666667  0.        ]]\n",
      "\n",
      " Matrix Division (M/N)   ==> \n",
      " [[ 1.          2.          3.        ]\n",
      " [ 2.         -1.5         3.        ]\n",
      " [ 2.33333333  2.66666667  0.        ]]\n"
     ]
    }
   ],
   "source": [
    "M = np.array([[1,2,3],[4,-3,6],[7,8,0]])\n",
    "N = np.array([[1,1,1],[2,2,2],[3,3,3]])\n",
    "\n",
    "print(\"\\n First Matrix (M)  ==>  \\n\", M)\n",
    "print(\"\\n Second Matrix (N)  ==>  \\n\", N)\n",
    "\n",
    "\n",
    "print(\"\\n Matrix Division (M/N)   ==> \\n\", M/N)\n",
    "\n",
    "# OR\n",
    "\n",
    "print(\"\\n Matrix Division (M/N)   ==> \\n\", np.divide(M,N))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Sum of all elements in a matrix"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 414,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      " Matrix (N)  ==>  \n",
      " [[1 1 1]\n",
      " [2 2 2]\n",
      " [3 3 3]]\n",
      "Sum of all elements in a Matrix  ==>\n",
      "18\n"
     ]
    }
   ],
   "source": [
    "N = np.array([[1,1,1],[2,2,2],[3,3,3]])\n",
    "\n",
    "print(\"\\n Matrix (N)  ==>  \\n\", N)\n",
    "\n",
    "\n",
    "print (\"Sum of all elements in a Matrix  ==>\")\n",
    "print (np.sum(N))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Column-Wise Addition"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 415,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      " Matrix (N)  ==>  \n",
      " [[1 1 1]\n",
      " [2 2 2]\n",
      " [3 3 3]]\n",
      "Column-Wise summation ==> \n",
      "[6 6 6]\n"
     ]
    }
   ],
   "source": [
    "N = np.array([[1,1,1],[2,2,2],[3,3,3]])\n",
    "\n",
    "print(\"\\n Matrix (N)  ==>  \\n\", N)\n",
    "\n",
    "print (\"Column-Wise summation ==> \")\n",
    "print (np.sum(N,axis=0))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Row-Wise Addition"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 416,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      " Matrix (N)  ==>  \n",
      " [[1 1 1]\n",
      " [2 2 2]\n",
      " [3 3 3]]\n",
      "Row-Wise summation  ==>\n",
      "[3 6 9]\n"
     ]
    }
   ],
   "source": [
    "N = np.array([[1,1,1],[2,2,2],[3,3,3]])\n",
    "\n",
    "print(\"\\n Matrix (N)  ==>  \\n\", N)\n",
    "\n",
    "print (\"Row-Wise summation  ==>\")\n",
    "print (np.sum(N,axis=1))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Kronecker Product of matrices"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Kronecker Product of matrices : https://www.youtube.com/watch?v=e1UJXvu8VZk"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 536,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1, 2, 3],\n",
       "       [4, 5, 6]])"
      ]
     },
     "execution_count": 536,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "M1 = np.array([[1,2,3] , [4,5,6]]) \n",
    "M1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 537,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[10, 10, 10],\n",
       "       [10, 10, 10]])"
      ]
     },
     "execution_count": 537,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "M2 = np.array([[10,10,10],[10,10,10]])\n",
    "M2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 538,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[10, 10, 10, 20, 20, 20, 30, 30, 30],\n",
       "       [10, 10, 10, 20, 20, 20, 30, 30, 30],\n",
       "       [40, 40, 40, 50, 50, 50, 60, 60, 60],\n",
       "       [40, 40, 40, 50, 50, 50, 60, 60, 60]])"
      ]
     },
     "execution_count": 538,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.kron(M1,M2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Matrix Vector Multiplication"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 418,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Matrix Vector Multiplication  ==> \n",
      " [[ 10  40  90]\n",
      " [ 40 100 180]]\n"
     ]
    }
   ],
   "source": [
    "A = np.array([[1,2,3] ,[4,5,6]])\n",
    "v = np.array([10,20,30])\n",
    "print (\"Matrix Vector Multiplication  ==> \\n\" , A*v)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Matrix Vector Dot Product"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 423,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Matrix Vector Multiplication  ==> \n",
      " [140 320]\n"
     ]
    }
   ],
   "source": [
    "A = np.array([[1,2,3] ,[4,5,6]])\n",
    "v = np.array([10,20,30])\n",
    "\n",
    "print (\"Matrix Vector Multiplication  ==> \\n\" , A@v)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Matrix Powers"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1, 2],\n",
       "       [4, 5]])"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "M1 = np.array([[1,2],[4,5]])\n",
    "M1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 57,  78],\n",
       "       [156, 213]])"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#Matrix to the power 3\n",
    "\n",
    "M1@M1@M1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 57,  78],\n",
       "       [156, 213]])"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#Matrix to the power 3\n",
    "\n",
    "np.linalg.matrix_power(M1,3)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Tensor"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "What is Tensor :\n",
    "   - https://www.youtube.com/watch?v=f5liqUk0ZTw\n",
    "   - https://www.youtube.com/watch?v=bpG3gqDM80w&t=634s\n",
    "   - https://www.youtube.com/watch?v=uaQeXi4E7gA"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 93,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[[  1,   2,   3],\n",
       "        [  4,   5,   6],\n",
       "        [  7,   8,   9]],\n",
       "\n",
       "       [[ 10,  20,  30],\n",
       "        [ 40,  50,  60],\n",
       "        [ 70,  80,  90]],\n",
       "\n",
       "       [[100, 200, 300],\n",
       "        [400, 500, 600],\n",
       "        [700, 800, 900]]])"
      ]
     },
     "execution_count": 93,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Create Tensor\n",
    "\n",
    "T1 = np.array([\n",
    "  [[1,2,3],    [4,5,6],    [7,8,9]],\n",
    "  [[10,20,30], [40,50,60], [70,80,90]],\n",
    "  [[100,200,300], [400,500,600], [700,800,900]],\n",
    "  ])\n",
    "\n",
    "T1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 94,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[[0, 0, 0],\n",
       "        [0, 0, 0],\n",
       "        [0, 0, 0]],\n",
       "\n",
       "       [[1, 1, 1],\n",
       "        [1, 1, 1],\n",
       "        [1, 1, 1]],\n",
       "\n",
       "       [[2, 2, 2],\n",
       "        [2, 2, 2],\n",
       "        [2, 2, 2]]])"
      ]
     },
     "execution_count": 94,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "T2 = np.array([\n",
    "  [[0,0,0] , [0,0,0] , [0,0,0]],\n",
    "  [[1,1,1] , [1,1,1] , [1,1,1]],\n",
    "  [[2,2,2] , [2,2,2] , [2,2,2]]\n",
    "    \n",
    "])\n",
    "\n",
    "T2"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Tensor Addition"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 95,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[[  1,   2,   3],\n",
       "        [  4,   5,   6],\n",
       "        [  7,   8,   9]],\n",
       "\n",
       "       [[ 11,  21,  31],\n",
       "        [ 41,  51,  61],\n",
       "        [ 71,  81,  91]],\n",
       "\n",
       "       [[102, 202, 302],\n",
       "        [402, 502, 602],\n",
       "        [702, 802, 902]]])"
      ]
     },
     "execution_count": 95,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "A = T1+T2\n",
    "A"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 96,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[[  1,   2,   3],\n",
       "        [  4,   5,   6],\n",
       "        [  7,   8,   9]],\n",
       "\n",
       "       [[ 11,  21,  31],\n",
       "        [ 41,  51,  61],\n",
       "        [ 71,  81,  91]],\n",
       "\n",
       "       [[102, 202, 302],\n",
       "        [402, 502, 602],\n",
       "        [702, 802, 902]]])"
      ]
     },
     "execution_count": 96,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.add(T1,T2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Tensor Subtraction"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 97,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[[  1,   2,   3],\n",
       "        [  4,   5,   6],\n",
       "        [  7,   8,   9]],\n",
       "\n",
       "       [[  9,  19,  29],\n",
       "        [ 39,  49,  59],\n",
       "        [ 69,  79,  89]],\n",
       "\n",
       "       [[ 98, 198, 298],\n",
       "        [398, 498, 598],\n",
       "        [698, 798, 898]]])"
      ]
     },
     "execution_count": 97,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "S = T1-T2\n",
    "S"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 98,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[[  1,   2,   3],\n",
       "        [  4,   5,   6],\n",
       "        [  7,   8,   9]],\n",
       "\n",
       "       [[  9,  19,  29],\n",
       "        [ 39,  49,  59],\n",
       "        [ 69,  79,  89]],\n",
       "\n",
       "       [[ 98, 198, 298],\n",
       "        [398, 498, 598],\n",
       "        [698, 798, 898]]])"
      ]
     },
     "execution_count": 98,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.subtract(T1,T2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Tensor Element-Wise Product"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 511,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[[   0,    0,    0],\n",
       "        [   0,    0,    0],\n",
       "        [   0,    0,    0]],\n",
       "\n",
       "       [[  10,   20,   30],\n",
       "        [  40,   50,   60],\n",
       "        [  70,   80,   90]],\n",
       "\n",
       "       [[ 200,  400,  600],\n",
       "        [ 800, 1000, 1200],\n",
       "        [1400, 1600, 1800]]])"
      ]
     },
     "execution_count": 511,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "P = T1*T2\n",
    "P"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 512,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[[   0,    0,    0],\n",
       "        [   0,    0,    0],\n",
       "        [   0,    0,    0]],\n",
       "\n",
       "       [[  10,   20,   30],\n",
       "        [  40,   50,   60],\n",
       "        [  70,   80,   90]],\n",
       "\n",
       "       [[ 200,  400,  600],\n",
       "        [ 800, 1000, 1200],\n",
       "        [1400, 1600, 1800]]])"
      ]
     },
     "execution_count": 512,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.multiply(T1,T2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Tensor Element-Wise Division"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 513,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "C:\\Users\\DELL\\Anaconda3\\lib\\site-packages\\ipykernel_launcher.py:1: RuntimeWarning: divide by zero encountered in true_divide\n",
      "  \"\"\"Entry point for launching an IPython kernel.\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "array([[[ inf,  inf,  inf],\n",
       "        [ inf,  inf,  inf],\n",
       "        [ inf,  inf,  inf]],\n",
       "\n",
       "       [[ 10.,  20.,  30.],\n",
       "        [ 40.,  50.,  60.],\n",
       "        [ 70.,  80.,  90.]],\n",
       "\n",
       "       [[ 50., 100., 150.],\n",
       "        [200., 250., 300.],\n",
       "        [350., 400., 450.]]])"
      ]
     },
     "execution_count": 513,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "D = T1/T2\n",
    "D"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 514,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "C:\\Users\\DELL\\Anaconda3\\lib\\site-packages\\ipykernel_launcher.py:1: RuntimeWarning: divide by zero encountered in true_divide\n",
      "  \"\"\"Entry point for launching an IPython kernel.\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "array([[[ inf,  inf,  inf],\n",
       "        [ inf,  inf,  inf],\n",
       "        [ inf,  inf,  inf]],\n",
       "\n",
       "       [[ 10.,  20.,  30.],\n",
       "        [ 40.,  50.,  60.],\n",
       "        [ 70.,  80.,  90.]],\n",
       "\n",
       "       [[ 50., 100., 150.],\n",
       "        [200., 250., 300.],\n",
       "        [350., 400., 450.]]])"
      ]
     },
     "execution_count": 514,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.divide(T1,T2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Tensor Dot Product"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 523,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[[  1,   2,   3],\n",
       "        [  4,   5,   6],\n",
       "        [  7,   8,   9]],\n",
       "\n",
       "       [[ 10,  20,  30],\n",
       "        [ 40,  50,  60],\n",
       "        [ 70,  80,  90]],\n",
       "\n",
       "       [[100, 200, 300],\n",
       "        [400, 500, 600],\n",
       "        [700, 800, 900]]])"
      ]
     },
     "execution_count": 523,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "T1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 524,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[[0, 0, 0],\n",
       "        [0, 0, 0],\n",
       "        [0, 0, 0]],\n",
       "\n",
       "       [[1, 1, 1],\n",
       "        [1, 1, 1],\n",
       "        [1, 1, 1]],\n",
       "\n",
       "       [[2, 2, 2],\n",
       "        [2, 2, 2],\n",
       "        [2, 2, 2]]])"
      ]
     },
     "execution_count": 524,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "T2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 533,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[  63,   63,   63],\n",
       "       [ 630,  630,  630],\n",
       "       [6300, 6300, 6300]])"
      ]
     },
     "execution_count": 533,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.tensordot(T1,T2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Solving Equations $$AX = B$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Solving Equations : \n",
    "   - https://www.youtube.com/watch?v=NNmiOoWt86M\n",
    "   - https://www.youtube.com/watch?v=a2z7sZ4MSqo"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 108,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1, 2, 3],\n",
       "       [4, 5, 6],\n",
       "       [7, 8, 9]])"
      ]
     },
     "execution_count": 108,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "A = np.array([[1,2,3] , [4,5,6] , [7,8,9]])\n",
    "A"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 109,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[0.4760653 ],\n",
       "       [0.69011595],\n",
       "       [0.27072528]])"
      ]
     },
     "execution_count": 109,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "B = np.random.random((3,1))\n",
    "B"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 110,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[-1.99693625e+15],\n",
       "       [ 3.99387250e+15],\n",
       "       [-1.99693625e+15]])"
      ]
     },
     "execution_count": 110,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Ist Method\n",
    "X = np.dot(np.linalg.inv(A) , B)\n",
    "X"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 111,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[-1.99693625e+15],\n",
       "       [ 3.99387250e+15],\n",
       "       [-1.99693625e+15]])"
      ]
     },
     "execution_count": 111,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# 2nd Method\n",
    "X = np.matmul(np.linalg.inv(A) , B)\n",
    "X"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 112,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[-1.99693625e+15],\n",
       "       [ 3.99387250e+15],\n",
       "       [-1.99693625e+15]])"
      ]
     },
     "execution_count": 112,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# 3rd Method\n",
    "X = np.linalg.inv(A)@B\n",
    "X"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 113,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[-1.99693625e+15],\n",
       "       [ 3.99387250e+15],\n",
       "       [-1.99693625e+15]])"
      ]
     },
     "execution_count": 113,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# 4th Method\n",
    "X = np.linalg.solve(A,B)\n",
    "X"
   ]
  }
 ],
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