math_practice.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np \n",
    "import matplotlib.pyplot as plt\n",
    "import seaborn as sns\n",
    "import pandas as pd"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Basic Vector Operations ( Addition, Subtraction, Multiplication by scaler ) and plotting them."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "sns.set()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.quiver(0,0,4,5)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.quiver(0,0,4,5,scale_units = 'xy',angles = 'xy', scale =1)\n",
    "plt.xlim(-8,8)\n",
    "plt.ylim(-8,8)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.quiver(0,0,4,5,scale_units = 'xy',angles = 'xy', scale =1,color = 'r')\n",
    "plt.xlim(-8,8)\n",
    "plt.ylim(-8,8)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.quiver(0,0,4,5,scale_units = 'xy',angles = 'xy', scale =1,color = 'g')\n",
    "plt.quiver(0,0,-2,8,scale_units = 'xy',angles = 'xy', scale =1, color = 'b')\n",
    "plt.xlim(-8,8)\n",
    "plt.ylim(-8,8)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[0 0 5 1]\n"
     ]
    }
   ],
   "source": [
    "vector_1 = np.asarray([0,0,2,3])\n",
    "vector_2 = np.asarray([0,0,3,-2])\n",
    "sum = vector_1 + vector_2\n",
    "print(sum)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.quiver(0,0,2,3,scale_units = 'xy',angles = 'xy', scale =1,color = 'g')\n",
    "plt.quiver(0,0,3,-2,scale_units = 'xy',angles = 'xy', scale =1, color = 'b')\n",
    "plt.quiver(0,0,5,1,scale_units = 'xy',angles = 'xy', scale =1,color = 'y')\n",
    "plt.xlim(-8,8)\n",
    "plt.ylim(-8,8)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[ 0  0 -1  5]\n"
     ]
    }
   ],
   "source": [
    "vector_1 = np.asarray([0,0,2,3])\n",
    "vector_2 = np.asarray([0,0,3,-2])\n",
    "diff = vector_1 - vector_2\n",
    "print(diff)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.quiver(0,0,2,3,scale_units = 'xy',angles = 'xy', scale =1,color = 'g')\n",
    "plt.quiver(0,0,3,-2,scale_units = 'xy',angles = 'xy', scale =1, color = 'b')\n",
    "plt.quiver(0,0,-1,5,scale_units = 'xy',angles = 'xy', scale =1,color = 'y')\n",
    "plt.xlim(-8,8)\n",
    "plt.ylim(-8,8)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[0 0 4 6]\n"
     ]
    }
   ],
   "source": [
    "vector_1 = np.asarray([0,0,2,3])\n",
    "vector_2 = 2*vector_1\n",
    "print(vector_2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.quiver(0,0,2,3,scale_units = 'xy',angles = 'xy', scale =1,color = 'g')\n",
    "plt.quiver(0,0,4,6,scale_units = 'xy',angles = 'xy', scale =1, color = 'b')\n",
    "plt.xlim(-8,8)\n",
    "plt.ylim(-8,8)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Dot Product , Cross Product, and projection of vectors."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "20\n"
     ]
    }
   ],
   "source": [
    "a = np.array([2,3])\n",
    "b = np.array([4,4])\n",
    "\n",
    "a_dot_b = a.dot(b)\n",
    "print(a_dot_b)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[16 -8 -4]\n"
     ]
    }
   ],
   "source": [
    "a = np.array([2,3,2])\n",
    "b = np.array([4,4,8])\n",
    "\n",
    "a_cross_b = np.cross(a,b)\n",
    "print(a_cross_b)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Projection of a vector on v vector is :  [1.5 1.5 3. ]\n"
     ]
    }
   ],
   "source": [
    "a = np.array([2 ,3 ,2 ])\n",
    "v = np.array([4 ,4 ,8 ])\n",
    "\n",
    "magnitude_of_v = np.sqrt(np.sum(v**2))\n",
    "proj_of_a_on_v = (np.dot(a,v)/magnitude_of_v**2)*v\n",
    "print(\"Projection of a vector on v vector is : \", proj_of_a_on_v)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Matrix Operations"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[2 3]\n",
      " [6 7]]\n"
     ]
    }
   ],
   "source": [
    "matrix_1 = np.array([[2,3],[6,7]])\n",
    "print(matrix_1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(3, 3)"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "matrix_1.shape\n",
    "matrix_2 = np.array([[2,3,4],[5,6,7],[8,9,10]])\n",
    "matrix_2.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[23 14 56 60 39]\n",
      " [ 9 44 17 47 94]\n",
      " [71  5 16 93  9]\n",
      " [36 33 84 10 69]]\n"
     ]
    }
   ],
   "source": [
    "# Random Values Matrix\n",
    "rand_matrix = np.random.randint(100,size =(4,5))\n",
    "print(rand_matrix)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[1 1 1]\n",
      " [1 1 1]\n",
      " [1 1 1]]\n"
     ]
    }
   ],
   "source": [
    "# Matrix with all values as 1\n",
    "\n",
    "matrix_3 = np.ones((3,3),dtype=int)\n",
    "print(matrix_3)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[0 0 0]\n",
      " [0 0 0]\n",
      " [0 0 0]]\n"
     ]
    }
   ],
   "source": [
    "matrix_4 = np.zeros((3,3),dtype=int)\n",
    "print(matrix_4)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[1 0 0 0 0]\n",
      " [0 1 0 0 0]\n",
      " [0 0 1 0 0]\n",
      " [0 0 0 1 0]\n",
      " [0 0 0 0 1]]\n"
     ]
    }
   ],
   "source": [
    "identity_matrix = np.identity(5,dtype=int)\n",
    "print(identity_matrix)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[41 66 19 87]\n",
      " [44  6 76 72]\n",
      " [51  2 84 92]\n",
      " [70 49 96 49]\n",
      " [34 91 98 70]]\n"
     ]
    }
   ],
   "source": [
    "trans_matrix = np.random.randint(100,size =(4,5))\n",
    "transpose_matrix = np.transpose(trans_matrix)\n",
    "print(transpose_matrix)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Matrix operations addition, subtraction, multiplication scaler and with other matrix"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[ 6  8]\n",
      " [10 12]]\n"
     ]
    }
   ],
   "source": [
    "a = np.array([[1,2],[3,4]])\n",
    "b = np.array([[5,6],[7,8]])\n",
    "c = np.add(a,b)\n",
    "print(c)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[-4 -4]\n",
      " [-4 -4]]\n"
     ]
    }
   ],
   "source": [
    "d = np.subtract(a,b)\n",
    "print(d)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[ 5 12]\n",
      " [21 32]]\n"
     ]
    }
   ],
   "source": [
    "e = np.multiply(a,b)\n",
    "print(e)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[ 8 16]\n",
      " [24 32]]\n"
     ]
    }
   ],
   "source": [
    "x = 8 \n",
    "f = np.multiply(a,x)\n",
    "print(f)"
   ]
  }
 ],
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