11-LinearAlgebra-Part2_solutions.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "e689afa4",
   "metadata": {},
   "source": [
    "# Linear Algebra (Part 2): Matrices and Eigenstuff\n",
    "\n",
    "\n",
    "### After completing this notebook, you'll be able to:\n",
    "* Construct and multiply matrices in Python (and by hand)\n",
    "* Create and manipulate special cases of matrices (unit matrix, diagonal matrix)\n",
    "* Explain matrices as a linear transformation and relate matrix properties to properties of that linear transformation\n",
    "* Define what eigenvalues/eigenvectors are and determine them using Python\n",
    "\n",
    "<hr>\n",
    "\n",
    "## Setup\n",
    "Below, we'll import a custom module with some **helper functions** to easily visualize vectors."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "a54e6752",
   "metadata": {},
   "outputs": [],
   "source": [
    "# Import modules, including a custom one!\n",
    "from matrices import *\n",
    "import numpy as np"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e639f00b",
   "metadata": {},
   "source": [
    "## Matrices\n",
    "\n",
    "A **matrix** is a rectangular array of numbers. The numbers in the matrix are **entries**. We can refer to each of the entries by their row and column.\n",
    "```\n",
    "A = [-1 -6  2\n",
    "      0  8  1]\n",
    "```\n",
    "You will sometimes see matrices referred to in mathematical notation. For example, a matrix $A$ could be denoted by $A = (a_{ij})$ where $a_{ij}$  is the entry in the $i^{th}$ row and $j^{th}$ column of matrix $A$. So for the matrix above, $A_{23}$ == 1.\n",
    "\n",
    "The **size** of the matrix is the number of rows multipled by the number of columns. $A$ is a 2x3 matrix, with a total size of 6. If a matrix has the same number of rows and columns, it is a **square** matrix. If it only has a dimension of one in one direction (e.g. 3x1), it is a **column matrix** (or **column vector**). \n",
    "\n",
    "The **transpose** of a matrix switches its rows and columns. The transpose (^T, or $^T$) of matrix $A$ above would be:\n",
    "```\n",
    "A^T = [-1 0\n",
    "       -6 8\n",
    "        2 1]\n",
    "```\n",
    "\n",
    "### Buiding matrices in NumPy\n",
    "We can build matrices in Python using numpy, using the following notation (notice there are parentheses to denote the array function, with brackets inside to indicate a list, with brackets inside *those* brackets for each row):\n",
    "\n",
    "```\n",
    "my_matrix = np.array([[row_1],[row_2],...[row_n]])\n",
    "```\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "dd3b1ae8",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1, 2, 3],\n",
       "       [4, 5, 6],\n",
       "       [7, 8, 9]])"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Build a 3x3 matrix\n",
    "my_matrix = np.array([[1,2,3],[4,5,6],[7,8,9]])\n",
    "my_matrix"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9827147e",
   "metadata": {},
   "source": [
    "Other useful matrix functions:\n",
    "* `np.random.randint()` builds a random matrix\n",
    "* `np.eye()` builds an **identity matrix**\n",
    "* `np.zeros()` builds a matrix of zeros\n",
    "* `np.ones()` builds a matrix of ones\n",
    "* `np.diag()` builds a **diagonal matrix**\n",
    "\n",
    "**Note**: Each of these differ in the inputs they take to instruct their size and shape -- always refer to the documentation!"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9007b5ad",
   "metadata": {},
   "source": [
    "We can also do matrix multiplication. In Python, we can use the `@` operator for matrix/vector multiplications. We can also use the NumPy [`np.dot`](https://numpy.org/doc/stable/reference/generated/numpy.dot.html#numpy.dot), [`np.matmul`](https://numpy.org/doc/stable/reference/generated/numpy.matmul.html). See the documentation for their differences."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "687476e4",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 52,  38,  16],\n",
       "       [130,  98,  40],\n",
       "       [208, 158,  64]])"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Create a random matrix\n",
    "random_matrix = np.random.randint(0,10,size=(3,3))\n",
    "\n",
    "# Use matmul for matrix multiplication\n",
    "np.matmul(my_matrix,random_matrix)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "2a9e75ff",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1., 0., 0.],\n",
       "       [0., 1., 0.],\n",
       "       [0., 0., 1.]])"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "identity = np.eye(3)\n",
    "print(identity)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "ec04c84d",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1., 2., 3.],\n",
       "       [4., 5., 6.],\n",
       "       [7., 8., 9.]])"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Use matmul for matrix multiplication with identity -- you get the same matrix back!\n",
    "np.matmul(my_matrix,identity)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0d6379e9",
   "metadata": {},
   "source": [
    "### Solving linear equations (abstract example):\n",
    "\n",
    "Let's say we have the following system of linear equations that we'd like to solve:\n",
    "\n",
    "$4x + 3y + 2z = 25$\n",
    "\n",
    "$-2x + 2y + 3z = -10$\n",
    "\n",
    "$3x - 5y + 2z = -4$\n",
    "\n",
    "We can use the inverse method, implemented using `np.linalg.inv()`. The **inverse** of a matrix (e.g., of $M$) is one that can be multiplied by it to produce an identity matrix. This is how we \"cancel\" a matrix in order to solve problems in the form $ Ax = b $."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "aa08fdca",
   "metadata": {},
   "outputs": [],
   "source": [
    "M = np.array([[4,3,2],[-2,2,3],[3,-5,2]]) # 3x3 co-efficients matrix\n",
    "K = np.array([[25],[-10],[-4]])           # column matrix\n",
    "V = np.array([['x'],['y'],['z']])         # unknown matrix"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0426ba75",
   "metadata": {},
   "source": [
    "$ M \\cdot V = K $\n",
    "\n",
    "so,\n",
    "\n",
    "$ V = M^{-1} \\cdot K$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "14563ea9",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 5.],\n",
       "       [ 3.],\n",
       "       [-2.]])"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "V = np.linalg.inv(M).dot(K)\n",
    "V"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d7ee41b6",
   "metadata": {},
   "source": [
    "### Coding Exercise 1.1: Understanding neural transformations using linear equations\n",
    "\n",
    "We will look at a group of 2 LGN neurons which get input from 2 retinal neurons: we will call the population of LGN neurons population $p$. Below, we have the system of linear equations that dictates the neuron models for each population. $r_1$ and $r_2$ correspond to the retinal neural activities (of neuron 1 and 2). $g_{p_1}$ and  $g_{p_2}$ correspond to the responses of the LGN neurons 1 and 2 in population $p$.\n",
    "\n",
    "\\begin{align}\n",
    "r_1 + 3r_2 &= g_{p_1} \\\\\n",
    "2r_1 + r_2 &= g_{p_2}\n",
    "\\end{align}\n",
    "\n",
    "<br>\n",
    "\n",
    "<div class=\"alert alert-success\"><b>Tasks:</b>\n",
    "    \n",
    "1. Cast each equation (i.e., $g_{p_1}$ and $g_{p_2}$) as a matrix-vector multiplication:\n",
    "\n",
    "\\begin{equation}\n",
    "\\mathbf{g}_p = \\mathbf{P}\\mathbf{r}\n",
    "\\end{equation}\n",
    "\n",
    "where $P$ is the weight matrix to population $p$.\n",
    "\n",
    "2. Let's say we only recorded from the LGN cells (and know the weight matrix) and are trying to figure out how the retinal cells responded. Solve the matrix equation for the given LGN activities:\n",
    "\n",
    "\\begin{equation}\n",
    "\\mathbf{g}_p =\n",
    "\\begin{bmatrix}\n",
    "16 \\\\\n",
    "7\n",
    "\\end{bmatrix}\n",
    "\\end{equation}\n",
    "</div>\n",
    "<br>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "2b972665",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[1. 5.]\n"
     ]
    }
   ],
   "source": [
    "# Create P (using np array)\n",
    "P = np.array([[1,3],[2,1]])\n",
    "\n",
    "# Create g_p (using np array)\n",
    "g_p = np.array([16,7])\n",
    "\n",
    "# Solve for r (using np.linalg.inv)\n",
    "r = np.linalg.inv(P).dot(g_p)\n",
    "\n",
    "# Print r\n",
    "print(r)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d00e7449",
   "metadata": {},
   "source": [
    "You can recover how the retinal neurons respond given the weight matrix and LGN responses! You have solved the system of equations using matrices. We can't always do this though: let's say we have a different group of 2 LGN neurons -  population q - with the following weight matrix from the retinal neurons.\n",
    "\n",
    "\\begin{equation}Q =\n",
    "\\begin{bmatrix}\n",
    "4 & 1 \\\\\n",
    "8 & 2\n",
    "\\end{bmatrix}\n",
    "\\end{equation}\n",
    "\n",
    "As you can see if you run the next code cell, we get an error if we try to invert this matrix to solve the equation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "c3de46fd",
   "metadata": {},
   "outputs": [
    {
     "ename": "LinAlgError",
     "evalue": "Singular matrix",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mLinAlgError\u001b[0m                               Traceback (most recent call last)",
      "\u001b[0;32m/tmp/ipykernel_195/3439701016.py\u001b[0m in \u001b[0;36m<module>\u001b[0;34m\u001b[0m\n\u001b[1;32m      2\u001b[0m \u001b[0mQ\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mnp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0marray\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;36m4\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;36m1\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m[\u001b[0m\u001b[0;36m8\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;36m2\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      3\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m----> 4\u001b[0;31m \u001b[0mprint\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mnp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mlinalg\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0minv\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mQ\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;34m@\u001b[0m \u001b[0mg_q\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m",
      "\u001b[0;32m<__array_function__ internals>\u001b[0m in \u001b[0;36minv\u001b[0;34m(*args, **kwargs)\u001b[0m\n",
      "\u001b[0;32m/opt/conda/lib/python3.9/site-packages/numpy/linalg/linalg.py\u001b[0m in \u001b[0;36minv\u001b[0;34m(a)\u001b[0m\n\u001b[1;32m    543\u001b[0m     \u001b[0msignature\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;34m'D->D'\u001b[0m \u001b[0;32mif\u001b[0m \u001b[0misComplexType\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mt\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;32melse\u001b[0m \u001b[0;34m'd->d'\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    544\u001b[0m     \u001b[0mextobj\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mget_linalg_error_extobj\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0m_raise_linalgerror_singular\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 545\u001b[0;31m     \u001b[0mainv\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0m_umath_linalg\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0minv\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0ma\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0msignature\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0msignature\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mextobj\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mextobj\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    546\u001b[0m     \u001b[0;32mreturn\u001b[0m \u001b[0mwrap\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mainv\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mastype\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mresult_t\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mcopy\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;32mFalse\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    547\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m/opt/conda/lib/python3.9/site-packages/numpy/linalg/linalg.py\u001b[0m in \u001b[0;36m_raise_linalgerror_singular\u001b[0;34m(err, flag)\u001b[0m\n\u001b[1;32m     86\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     87\u001b[0m \u001b[0;32mdef\u001b[0m \u001b[0m_raise_linalgerror_singular\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0merr\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mflag\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 88\u001b[0;31m     \u001b[0;32mraise\u001b[0m \u001b[0mLinAlgError\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m\"Singular matrix\"\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m     89\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     90\u001b[0m \u001b[0;32mdef\u001b[0m \u001b[0m_raise_linalgerror_nonposdef\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0merr\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mflag\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;31mLinAlgError\u001b[0m: Singular matrix"
     ]
    }
   ],
   "source": [
    "g_q = np.array([16, 7])\n",
    "Q = np.array([[4, 1], [8, 2]])\n",
    "\n",
    "print(np.linalg.inv(Q) @ g_q)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "id": "87f7922a",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAS8AAAEoCAYAAAAJ23dgAAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjQuMiwgaHR0cHM6Ly9tYXRwbG90bGliLm9yZy8rg+JYAAAACXBIWXMAAAsTAAALEwEAmpwYAAAiQklEQVR4nO3deXxU5aE+8OfMko0QSEYikAECIiQmmaQgmyAClUGWQtHWouVeW+x1uXpV9GLbqFdxAbV6q73W+rNqa2tjlLpAAYOCiIAogmDYDNBmIJOADJMEksAks7y/P04WIgmTSWbmnTPzfD8fP+ZMzpx5MhOevGdXhBAgItIanewARETdwfIiIk1ieRGRJrG8iEiTWF5EpEksLyLSJJYXdZuiKHpFUXYpirJadhaKPSwv6om7ARyQHYJiE8uLukVRFDOA2QBekZ2FYhPLi7rrOQD3A/BJzkExytCTJ+/cuVOYTKZgZek2p9OJSMgBxEaWDRs2YOHChXjssceu+/zzz/HHP/4RNpvtvPPMioqKUFxcDABoaGjAhg0bgp6lO2R/RiW707D7aDK8Ph0Agcx+Lvx04rfS8rSQ/b6cKzMzU/E3T4/Ky2QyITMzsyeLCJpIyQFEf5bDhw9j48aNmDJlClwuF06fPo0HH3wQb7zxRrv5CgsLUVhYCACwWCxR/750RU09UFoBeJvHqwadwE3WRJj7ycnzXZH0GfnD1UYK2PLly2G322Gz2VBcXIxp06adV1zUsZWfAb7mMaqiAJn9XDD3k5tJq1heRGHiPA1sLzt31AV8P7dGbigN69FqI9GUKVMwZcoU2TE04d2tbcWlU4C8ocBFvd1yQ2lY0MvL7XbDbrfD5XIFe9Gd8ng8OHAgPIcbJSQkwGw2w2g0huX1KDqcqAV2HW5bZdTrgesmAWdqZabStqCXl91uR+/evZGZmQlF8bvDICgaGxsRHx8f8tcRQsDpdMJut2Po0KEhfz2KHn/f3H7U9b1LgPS+gK1WZiptC/o2L5fLBZPJFLbiCidFUWAymcI6qiTtq3ICe23njLp0wLUTpUaKCiHZYB+NxdUimn82Co2/bwY8zaMuvQ4YOxIwpcjNFA2k7238zQr1r9K51n8F/O3jwJZz9ASwp7zneZ57D7jrReB3K3u+LKIKB/CNHWi5VYROB8y7Qm6maCG9vMaOBL482P6x7QeBMSMDW06FA9hjC+w53g5ObJkxGrj5msCWQ9SZFZ8CHo/6tUEPTLwMSE2WmylaSD9UYvSlwPvbALcHMBqAk6eAUw3ApQOBfUeAVdsAjxfo1xf42XQgIQ4oPw68tQlodKu/EHfMBlZ9DjR5gEOVwKwxwGVDgD9/CDhOA3EG4N+/D5j7qcurbVCPuUlOBP5jZvs82YOBsgopbwVFmfLjwOFjQMt5U4oC/GC81EhRRXp5JScCQy9Wi6rgEnUUdvkIoN4FrNkO3HsdEG8EPvgS+OgrYOYY4OW1wC2zgKH9gbONgPABc8cDR04AN05Vl1u0ERiUDtwxFzhQAby6Dnh4ofq9IyeAX16vlhpRqLz9qfpHGVD/yE7JA1KS5GaKJhHxz3fsSPXI44JL1P//zAr86xhwzAk8+ZY6j9cHDBsAHK8B+vRSiwsAEuOBxsbzl3m4Crh9jvp19iCgwQWcaZ4vfxiLi0LrcJW6HbaFTgFmjZWXJxpFxD/hgkvUv1JHTgBuLzAkHaitV1fhbpnVfl67Qx1++9PRvXRbnhbP40spxN7apG7GAACjHvh+gbqWQcEjfYM9oG7HGmFWt1GNHaE+Nqw/8M9j6pHJgLp963gN0D9NLbby4+rjriZ1VJYQp37dYoQZ+OIb9euyCvUXJzH0x7ES4UCFemxXC50OuOZyeXmiVUSMvAB11fEPq9tGWr2T1NXHlz9QN9gDwA8nAP1T1Xne/KRtI/+dc4CsQcAHO4Clb6gb7OeOB/70IfDIG+oq4iJr13I89bZako1NwJJXgJuuBnIzQ/ETUzQSAnj73FGXQd2DnZQgN1c0ipjyGjUc+OM97R/LHgQ8eMP58w7tDxQuaJtubATi48+f98655z937oQL5/jl9V2KS9ShfUcAx6m2ab0OmD5KXp5oFhGrjUTRQIi2Q3gAdcQ/e4y6SYOCj+VFFCRf/0u9UmoLgx6YWiAtTtRjeREFgU8Ab316zqjLqB6Qyj3bocPyIgqCnQeBujNt00Y9cFWevDyxgOVF1EM+H7Bic9uoK94IzJ+o7mmk0GF5EfXQF2VtZ28AanlNvExenlghvbwq/+1POLP5cLvHav+8DY5HVge0nMYDx9Cw6aD/Gf0sw/6TV3B09u9R8YMXUb92b4+WR9HP41Wv13XuqOvaierGegot6eWVPDvvvJKoX7sXyXMC22DQeOA4zmw6FNBzRMvRr82UBCPSn5qPwWvuwIBXFuLkshJ4T58NaJkUWz7b31ZcgHoWx/hseXliifS18uQZl6H6uY8hmjxQ4gxw22vgPVGHhNGDcWbLYVT/3ycQTR4YB6Uhffk86HrFw1VaiZPLPoA444YSp4fppZ+g5ncb4XN54Np5FKm3XonEK4bhROFKeCpqoCQa0e/RHyA+qz+q/28jPCfq4KmshT41CRc/+6PWLHFDL2r92nBxCvRpveCtPgN9Ck9Ko/O5PcB7W9uPun40ST0wlUJPennpU5OQYMnAmU8Po9fVWahfuxe9ZubCV3MGNX/4FAP/9O/QJcWh5uUtqP3TNqTeMgnfLl6Bi3/7YyRYMuCrd6FJEUi9ayoa91ah3//MBgA4HluL+MsGYMCLN+DMtn/hxC/fw6CVtwMAGvcdQ0bRIugSOt+P7Sq1Q7i9MA5ODcv7QNqzeW/baUCAev5soBfRpO6LiL8RybNzW1cd69fsRe85uXB9bUfTYQcqb3gVFfP+gLr3d8NTdQpN5U4Y+vVGgiUDAKBLToBiOP/HcO08it7zLACApAnD4K09C2+deuOMXtNGXrC4PCfqcGLJe0hfPg+KLiLeIoowTR5g5ba28oo3AtdfqV76hsJD+sgLAHpdnYWTT65D474qCJcH8TkD4fm2DEkTL8HF//ujdvM2fnO87do2F9LBNXFaLqWjS+y8uHz1Lhy79W9Iu2caEgoGBfJjUAzZuLvtggEA0LcX8L3h0uLEpIgYVuh6xSNxbCZOFK5E8pxcAEBCgRmur47CfUS9tojvbBOayk8ibthF8Jyog6u0Un28vhHC44OuVzx8DW3XxEkcMwR1q/YAAM5+UQ59ahJ0yRc+tV80eXD8jrfQe14+kmfmhOJHjQoulwtjx45Ffn4+cnJy8PDDD8uOFFauJmD19vajrp9c1bXrzFHwRMTICwCS5+Th2zvfah1p6dN6od/yH+Lbe9+BaP4tSbtnGuKGXoSLf/tjnHx8LYTLAyXBANP/W4DEcZmofXkLKub9Aam3XonUO6fgxK9XouIHL0JJNCL9yR/6zVD/wT6c3XEE3tozqHtvNwAg/ckfIj57QKh+bE2Kj4/Hxx9/jOTkZLjdbkyaNAkzZ87E+PGxcYH29bvUA1NbmFJ42SQZIqe8pmcjueyRdo8lTRiGpHduOW/eBEsGzG//R+t0Y2Mj9PHxMH9n3gF/OP96Omn/NbXTDL3n5aP3vPwAk8ceRVGQnKzeAsftdsPtdsfM/SzPNgIlO9pGXXEcdUkTEauNpD1erxcFBQVIT0/H9OnTMW7cONmRwmLdzrY7XwPqxTGzuWlUih6NvJxO53mPeTweNHZ0R4wQ8ng8/mcK8uvZbLYOv9fReyJLqLO8//77OH36NG699VasW7cOI0e2P06gqKgIxcXFAACHw9HpexZu3X1fzjbp8OFOM9xe9W++Ue/DVSO+xZEj3f99j6Xfl0BkZmb6nadH5WUymc57kQMHDiA+PvwXiw/naxoMhgu+uV1548MlHFmuueYa7NmzBzNmzGj3eGFhIQoLCwEAFotF8+/Lik/bTw9O12Hy5T3fHqr190WWkKw2io5u3RMlovln6yqHw4Ha2loAwNmzZ7F+/XpkZWXJDRVidWeAjaXq3a0A9SqpP7lKbqZYF/QN9gkJCXA6nTCZTFG3EVcIAafTiYSE2L6bwrFjx3DTTTfB6/XC5/Ph+uuvx5w5c2THCql/fKHe3LjF0P5t9w4lOYJeXmazGXa7HQ6HI9iL7pTH44HBEJ4dpwkJCTCbzWF5rUhlsViwa9cu2THCprYB2LIX8DSXl9EAXD9ZbiYKQXkZjUYMHTo02Iu9IJvNpql1ddKWVdva9jAqCjAiAxicLjcT8VAJogtyngY+P6De2BgADDrgxxx1RQSWF9EFvP9Z26hLpwA5mUCGSWokasbyIuqE4xSw81DbqEuvA66bJDcTtWF5EXXinS1txaVTgIJL1CPqKTKwvIg6cKwaKP1X2yqjXqfeEYgiB8uLqAPvbG6/ujhmBNCvj9xM1B7Li+g77CeB/RXtN9TPu0JuJjofy4voO1Z8CrSc66/XAROygbTecjPR+VheROc48i1wqApoOYNVpwPmTpAaiTrB8iI6x1ufqrc0A9Qbx07OBfr0kpuJOsbyImr2zyp15NVCpwCzY+Mai5rE8iJq9vanbZd3NuqBaQVAb95vOGKxvIgAlNnVvYwtdDrgmsvl5SH/WF4U84QA3trUftRlHQX0iu3LtkU8lhfFvP1HgW9r2qb1OsA6Wl4e6hqWF8W074664gzAzLFAQpzcXOQfy4tiWmk5UF3XNq3XAd8vkBaHAsDyopjlE8Dbm4BGtzodZwDmjAPijXJzUdewvChmfXUIOHWmbdpoAKbyhumawfKimOTzASs2t4264o3AvAlqgZE2sLwoJm0vAxpcbdNxBuDKXHl5KHAsL4o5Ph/w9y3tR13zJ6rnMpJ2sLwo5pQeTcbZxrbphDjgisvk5aHuYXlRTPF4gY37U1uP64o3Aj+apB4iQdrCj4wCVlFRgalTpyI7Oxs5OTl4/vnnZUfqss17AbdXaZ3ulQCMHSkxEHUb961QwAwGA5599lmMGjUKdXV1GD16NKZPn47LLovsdS+3B1i5DXB71b/Z8Ubgx1eqJ2GT9vBjo4ANGDAAo0aNAgD07t0b2dnZqKyslJzKv09K2y40CAApScCoS+XloZ5heVGP2Gw27Nq1C+PGRfZV+xrdwD8+B9Iq7TC6mxBvBH5ylXrBQdKmHq02Op3OYOXokUjJAcRWloaGBixYsACFhYWorq5GdXV1u+8XFRWhuLgYAOBwOGCz2UKa50I+O5iC4XuPYtaGlVg7dS6OjclBilIFiZEAxNbvSyAyMzP9ztOj8jKZTF16kXCIlBxAbGRxu92YM2cOfv7zn+O2227rcJ7CwkIUFhYCACwWi7T3xdUEnHr6K1g/WQuvTofTaWlYeHUchg6Rk+e7YuH3JRS42kgBE0Lg5ptvRnZ2Nu69917Zcfz68jdfYuqmtTB61Q1eYmAKLhssORT1GMuLArZ161b89a9/xccff4yCggIUFBRg7dq1smN16MSrn6Nf0ToYm2/EKHQKJo87C4XbujSPh0pQwCZNmgQhhP8ZJav54xac+t2m1uICgLN9+mBIvyaJqShYWF4Ulap//wlqXt4KXZO73eMpWRdJSkTBxtVGiipCCDh/uwG1L28FXO2LSyhAasHFkpJRsHHkRVFDCAHnUx/i9Js7IL5TXACgJMbBOKyfhGQUChx5UdSo/t8NnRYXACg6BcYhaWFORaHC8qKooSTFqbcDMnZ8YS7hcsOYaQpzKgoVlhdFjbTbJ2Pw+rtxJrUvOtoXqsQboO/NO8lGC5YXRRXnSQ/inKfQchiX22BUr/EMwJjRV1ouCj6WF0WVw0vXQ/F5AQBeRYfaEUPR9+fjoSQYEJ87UHI6CibubaSoUfW1E6Y9ZdA3H0Dr0+mQ+dg1MOWmIfXWK6Ek8oaM0YQjL4oatkc/gu6cUZfze5ehf666d1HXKx4KrzoYVfhpUlSo+PIE0g4cbjfqGvHwNMmpKJRYXhQV7I99CH3zqMuj08M5Ng/9RvSVG4pCiuVFmndk6zGkHrZB1zzqEoqC7EemSk5FocbyIs079vg66Juv1eXR6eG88ntIy0yRnIpCjeVFmvbPj+3oe9Te+ossdApyH7pKaiYKD5YXadrJZetgaL5el0evR/XUMehjTpacisKB5UWadfCDI+hz7Hjr0fRC0SHvoSulZqLwYXmRJvl8AqeeKoHRo15Bwq03oHrGePS+OElyMgoXlhdp0sFV5Uh2nGydFjoFlsKJEhNRuLG8SHN8PoH6Z0oQ1zLqMhhQO3cSki/iFSNiCcuLNOfAikPoVVPTOu3T6ZF//3iJiUgGlhdpis8n0PjcutZRV5PBiLrrJiOpb7zkZBRuLC/SlL1//QaJp0+3Tvv0euT/91iJiUgWlhdphtfrg/f37UddDTdORUIyL3UTi1hepBl7XtuHhDMNrdNegxEFd42WmIhkYnlRtyxatAjp6enIzc0Ny+t5mrxQXvoIce7mUZfRCNdN0xCXxOtpxiqWF3XLz372M5SUlITt9Upf3oO4xrOt025jPPL/83the32KPCwv6pbJkycjLS0890B0u7wwvnrOqMtghOcXV8OY0PEtzig2sLwo4n39+10wNDW1TjclJiL/FovERBQJerTBwOl0BitHj0RKDiC2stjtdrjdbthstg6/X1RUhOLiYgCAw+HodL4L8bi8SPjLhnZ7GE/dOA4VlUe7GzumPqNARFKWzMxMv/P0qLxMJlOXXiQcIiUHEFtZjEZjp69RWFiIwsJCAIDFYulWli+WfY6U5kveAIArORkT754Avb5nKw2x9BkFIpKy+MPVRopYrjo3kos/aRt1GY0w3GntcXFRdOBvAXXLDTfcgAkTJqCsrAxmsxmvvvpq0F9j9zPbofN6W6fP9O6DnJ9mBf11SJt4kAx1y5tvvhnS5Z+pbUTKu5+2G3Ul3jsDOp3i55kUKzjyooj09ZPbWm8gCwANqanIum64xEQUaVheFHHqT7rQd/VWGJs31DcZjEhecg1HXdQOy4siTumyLVB8onW6Lr0fsuYOk5iIIhHLiyLK6WNnkLbuCxib78PoNhiR9qtrJKeiSMTyooiy5/HNQMudrwGcGtgfw2cMlhuKIhLLiyJGrb0epk++bB11eQwG9CvkqIs6xvKiiLFv6Set27p8AGqGDMKwqRlyQ1HEYnlRRKguP42Ltu6GofnwCK/egIEPzpCciiIZy4siwoGlGwHhAwD4FAXVw4diyBX9JaeiSMbyIukcZbW4aPseGHxqeXl1egx5eLrkVBTpWF4k3cGlG6C0FJeiwJk9HBmj0yWnokjH8iKpju9x4qLdB6BvXmUUOj0ueYSjLvKP5UVS/fPR9VBaNtIrCk7mZ6F/nklyKtIClhdJU/mVA6Z9h6BvOShVp8eIR66WnIq0guVF0hx59EPoW0ZdOh1OXp6LfiP7yg1FmsHyIimObjuOtEPl0DWPunyKDlmPTJOcirSE5UVSVD62DvrmS954dHo4ryiAaViK5FSkJSwvCrvyTZVIPWJv/eUTOgU5/zNFZiTSIJYXhd23T6yDofnyzm69Hs4pl6Pv4GTJqUhrWF4UVoc/PIq+lcfQek1URYe8ByfLjEQaxfKisKp+ch2MraMuA6qt45AyIElyKtIilheFTdk/ytH72xOt00KnwPLriRITkZaxvCgshA84/ZuS1luZufUG1M6eiOT0RMnJSKtYXhQWuZ6LkVxd3TotdDrk/3qCxESkdbzpLIWczyfwC68FcaJ51GUw4tS1VyKpb7zkZKRlHHlRt5SUlGDkyJEYPnw4nnzyyQvOu+/NMqQrbauHPp0O+f89LtQRKcqxvChgXq8Xd9xxBz744APs378fb775Jvbv39/JvD64f7cOSYo6yG8yGFG/YAoSU+LCGZmiEMuLArZ9+3YMHz4cw4YNQ1xcHBYsWICVK1d2OO+eP+9HYkN967TXYEDB4jHhikpRjOVFAausrMSgQYNap81mMyorKzuct7HqNBSfgFf40GQw4uzCaYhL4qZW6jlFCOF/rk7k5OQIvV4fxDjdc+rUKfTp00d2DACxkaW2thb19fUwm80AgJqaGpw9exYDBw5sN5/T6URNTQ2y4jPwn8njMDghHffHb4BP1/3fuWCIhc+oOyIpy549e/YJIXIvOJMQotv/5eXliUgQKTmEiI0sn332mbBara3Ty5YtE8uWLbvgcxITE0OSpTti4TPqjkjKAmCH8NM/XG2kgI0ZMwaHDh1CeXk5mpqaUFxcjLlz58qORTGGGx8oYAaDAS+88AJmzJgBr9eLRYsWIScnR3YsijE9Kq8FCxYEK0ePREoOIHayzJo1C7Nmzery/KmpqSHLEqhY+YwCFUlZALzsb4YebbC32WwiMzOz288PFpvNhkjIATBLZywWC0pLS2XHABBZ7wuzdErxNwO3eRGRJgWlvJ555hkoioKTJ08GY3Hd8tBDD8FisaCgoABWqxVVVVXSsixZsgRZWVmwWCyYP38+amtrpWVZsWIFcnJyoNPpsGPHDikZSkpKUFZW1qVTiUJp0aJFSE9Px4wZM6RlAICKigpMnToV2dnZsFqteP7556VlcblcGDt2LPLz82G1WvHwww9Ly9LC6/VCUZRdiqKsvuCM/nZHXui/8vJycfToUWG1WsXgwYOFw+EI377Uc5SXl4tTp061Tj///PPi1ltvlZZl3bp1wu12CyGEuP/++8X9998vLcv+/fvFN998I6666irx5Zdfhj2Dx+MRw4YNEyNHjhSNjY3CYrGIffv2hT2HEEJs2rRJ7Ny5U4wYMULK67eoqqoSO3fuFEIIsWfPHnHppZdKe098Pp+oq6sTQghx8OBBMXbsWLFt2zYpWVo8++yzAkARgNUilIdKLF68GE8//TQUxe8qakilpLTdeaahoUFqHqvVCoNB3Rcyfvx42O12aVmys7MxcuRIaa/fcipRXFyc31OJQm3y5MlIS0uT8trnGjBgAEaNGgUASE5ORnZ2dqdnKISaoihITlbvH+DxeOB2u6X+27Hb7VizZg0AvOJv3h6V10cffYSMjAzk5+f3ZDFB88ADD2DQoEH429/+hkcffVR2HADAa6+9hpkzZ8qOIU0gpxLFIrvdjl27dmHcOHlX2fB6vSgoKMDll1+O6dOnS81yzz334OmnnwYAn795/R4qoSjKegD9O/jWA/n5+di0aVPgCbvp6quvxvHjx897/K677sItt9yCJ554Ak888QSWL1+OF154AUuXLpWWBQCeeOIJGAwG/PSnPw1Zjq5mkUV0sDdb9ig9UtTX1+P222/Hc889127NIdz0ej12796N0tJS3H333di7dy9ycy98Zk4orF69Gunp6Rg9enSX5vdbXkKIqzt6XFGUPLvd3jrqstvtGDVqFLZv347+/Tvqup5bv359h4/bbLZ20zfeeCNmz54d0vLyl+X111/H6tWrsWHDhpD/Y+3q+yKD2WxGRUVF67Tdbj/vHMhY5Ha7cd1112HevHm49tprZccBoG56mTJlCkpKSqSU19atW7Fq1SqsXbsWAIoBpCiK8oYQYmFH83d7tVEIsWfHjh2w2Wyw2Wwwm8346quvQlZc/hw6dKj161WrViErK0tKDkDdu/bUU09h1apVSEqK7TvjtJxK1NTUxFOJmgkhcPPNNyM7Oxu/+MUvpGZxOByte8NdLhfWr18v7d/O8uXLYbfbW/7oLgDwcWfFBaDnextbDBkyROrexmuvvVbk5OSIvLw8MWfOHGG326VlueSSS4TZbBb5+fkiPz9f6p7Pd999V2RkZIi4uDiRnp7e7oTqcFmzZo2Ii4sTw4YNE48//njYX7/FggULRP/+/YXBYBAZGRnilVdekZJj8+bNAoDIy8sT2dnZIj8/X6xZs0ZKlq+//loUFBSIvLw8MWLECLF06VIpOb4LwBT42dvII+yDjFk6xiPsO8YsneIR9kQUnVheRKRJLC8i0iSWFxFpEsuLiDSJ5UVEmsTyIiJNYnkRkSaxvIhIk1heRKRJLC8i0iSWFxFpEsuLiDSJ5UVEmsTyooBEwq3UiACWFwUoNzcX7777LiZPniw7CsU4v9ewJzpXdna27AhEADjyIiKN6tHIy+l0BitHj0RKDiA6sixcuBAOh+O8x++77z5YrVYA6s0aqqqqLniHoqKiIhQXFwNQb/QQCXczAqLjMwqFSMrSlctR96i8TCZTxFzzOlJyANrPsmXLFr/zJCQkYODAgRdcfmFhIQoLCwGo17DX+vsSKszSPVxtJCJNYnlRQN577z2YzWZs27YNs2fPxowZM2RHohjFvY0UkPnz52P+/PmyYxBx5EVE2sTyIiJNYnkRkSaxvIhIk1heRKRJLC8i0iSWFxFpEsuLiDSJ5UVEmsTyIiJNYnkRkSaxvIhIk1heRKRJLC8i0iSWFxFpEsuLiDSJ5UVEmsTyIiJNYnkRkSaxvIhIk1heRKRJLC8i0iSWFxFpEsuLiDSJ5UVEmsTyooAsWbIEWVlZsFgsmD9/Pmpra2VHohjF8qKATJ8+HXv37kVpaSlGjBiB5cuXy45EMYrlRQGxWq0wGAwAgPHjx8Nut0tORLGK5UXd9tprr2HmzJmyY1CMMvTkyU6nM1g5eiRScgDRkWXhwoVwOBznPX7ffffBarUCAF544QU0NTVh4sSJsNlsHS6nqKgIxcXFAACHw9HpfOEWDZ9RKERSlszMTL/zKEKIbr+AzWYTXXmRULPZbF36YcMhFrK8/vrreOmll7BhwwYkJSV16TkWiwWlpaVBz9IdsfAZdUckZQGg+JuhRyMvij0lJSV46qmnsGnTpi4XF1EocJsXBeTOO+9EXV0dpk+fjoKCAtx2222yI1GM4siLAnL48GHZEYgAcORFRBrF8iIiTWJ5EZEmsbyISJNYXkSkSSwvItIklhcRaRLLi4g0ieVFRJrE8iIiTWJ5EZEmsbyISJNYXkSkSSwvItIklhcRaRLLi4g0ieVFRJrE8iIiTWJ5EZEmsbyISJNYXkSkSSwvItIklhcRaRLLi4g0ieVFRJrE8qKAPPTQQ7BYLCgoKIDVakVVVZXsSBSjWF4UkCVLlqC0tBS7d+/GnDlz8Oijj8qORDGK5UUBSUlJaf26oaEBiqJITEOxzCA7AGnPAw88gL/85S/o06cPNm7cKDsOxShFCNHtJ+/cuVOYTKYgxukep9OJSMgBREeWhQsXwuFwnPf4fffdB6vV2jr94osvorGxEYsXL+5wOUVFRSguLgYAOBwObNu2LeAsoRANn1EoRFKWzMxMv0P6HpWXzWYTmZmZ3X5+sNhsNkRCDiC2shw5cgSzZ8/G3r17/c5rsVhQWloasiyBiKXPKBCRlAWA3/LiNi8KyKFDh1q/XrVqFbKysiSmoVjGbV4UkF/96lcoKyuDTqfDkCFD8NJLL8mORDGK5UUBeeedd2RHIALA1UYi0iiWFxFpEsuLiDSJ5UVEmsTyIiJNYnkRkSaxvIhIk1heRKRJLC8i0iSWFxFpEsuLiDSJ5UVEmsTyIiJNYnkRkSaxvIhIk1heRKRJLC8i0iSWFxFpEsuLiDSJ5UVEmsTyIiJNYnkRkSaxvIhIk1heRKRJLC8i0iSWF3XLM888A0VRcPLkSdlRKEaxvChgFRUV+OijjzB48GDZUSiGsbwoYIsXL8bTTz8NRVFkR6EYxvKigKxatQoZGRnIz8+XHYVinCKEkJ2BIoyiKOsB9O/gWw8AKARgFUKcUhTFBuByIUSHG74URbkFwC3NkwlCiNxQ5KXYxPKiLlMUJQ/ABgBnmh8yA6gCMFYIcVxaMIpJLC/qNn8jL6JQ4jYvItIkjryISJM48iIiTWJ5EZEmsbyISJNYXkSkSSwvItIklhcRaRLLi4g0ieVFRJr0/wFeNl5doTjJ/QAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 360x360 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "from linear_algebra import *\n",
    "\n",
    "# Vectors are overlaid (same if you use 4,1 and 8,2)\n",
    "visualize_vectors([4,8],[1,2])"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "77990fce",
   "metadata": {},
   "source": [
    "## Matrices as linear transformations\n",
    "\n",
    "For now, let's start to think about all of this as **[linear transformations of matrices](https://www.youtube.com/watch?v=N6UUV9tVIr8)**. \n",
    "\n",
    "Matrices can be thought of as enacting linear transformations. When multiplied with a vector, they transform it into another vector. In fact, they are transforming a grid of space in a linear manner: the origin stays in place and grid lines remain straight, parallel, and evenly spaced."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e7389af4",
   "metadata": {},
   "source": [
    "### Coding Exercise 1.2: Creating matrices for transformations\n",
    "\n",
    "<div class=\"alert alert-success\"><b>Tasks:</b>\n",
    "\n",
    "1. Come up with a matrix $A$ for which the corresponding linear transformation is reflection through the $y$ axis (flipping across the $y$ axis). For example, $\\mathbf{x} = \\begin{bmatrix}\n",
    "2 \\\\\n",
    "6  \\\\\n",
    "\\end{bmatrix}$ should become $\\mathbf{b} = \\begin{bmatrix}\n",
    "-2 \\\\\n",
    "6  \\\\\n",
    "\\end{bmatrix}$ when multiplied with $A$.\n",
    "2. Come up with a matrix $B$ for which the corresponding linear transformation is projecting onto the $x$ axis. For example, $\\bar{x} = \\begin{bmatrix}\n",
    "2 \\\\\n",
    "3  \\\\\n",
    "\\end{bmatrix}$ should become $\\bar{b} = \\begin{bmatrix}\n",
    "2 \\\\\n",
    "0  \\\\\n",
    "\\end{bmatrix}$ when multiplied with $B$.\n",
    "\n",
    "</div>\n",
    "\n",
    "**Remember to think about where your basis vectors should end up! Then your matrix consists of the transformed basis vectors. Drawing out what you want to happen can help**"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "id": "88e6fe4a",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 3000x1400 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "A = np.array([[-1,0],[0,1]])\n",
    "\n",
    "# Uncomment to visualize transformation\n",
    "plot_linear_transformation(A)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "id": "3c299a6f",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 3000x1400 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "B = np.array([[1,0],[0,0]])\n",
    "\n",
    "# Uncomment to visualize transformation\n",
    "plot_linear_transformation(B)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0074acc3",
   "metadata": {},
   "source": [
    "## Eigenvalues & Eigenvectors"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ddc7347c",
   "metadata": {},
   "source": [
    "[**This video**](https://www.youtube.com/watch?v=l-c7ptT7znM) covers eigenvalues and eigenvectors.\n",
    "\n",
    "Eigenvectors $\\mathbf{v}$ of a matrix $\\mathbf{W}$ are vectors that, when multipled by the matrix, equal a scalar multiple of themselves. That scalar multiple is the corresponding eigenvalue $\\lambda$.\n",
    "\n",
    "\\begin{equation}\n",
    "\\mathbf{W}\\mathbf{v} = \\lambda\\mathbf{v}\n",
    "\\end{equation}\n",
    "\n",
    "If we have one eigenvector for a matrix, we technically have an infinite amount: every vector along the span of that eigenvector is also an eigenvector. So, we often use the unit vector in that direction to summarize all the eigenvectors along that line.\n",
    "\n",
    "We can find the eigenvalues and eigenvectors of a matrix in numpy using `np.linalg.eig`."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b468b3a8",
   "metadata": {},
   "source": [
    "### Identifying transformations from eigenvectors\n",
    "\n",
    "Earlier, we learned how to think about linear transformations in terms of where the standard basis vectors end up. We can also think about them in terms of eigenvectors.\n",
    "\n",
    "Just by looking at eigenvectors before and after a transformation, **can you describe what the transformation is in words (e.g.contraction, expansion, horizontal vs vertical, projection onto an axis, reflection, and rotation)**? Try for each of the two plots below.\n",
    "\n",
    "Note that I show an eigenvector for every eigenvalue. The $x/y$ limits do not change in before vs after (so eigenvectors are showed scaled by the eigenvalues)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "id": "ff477884",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 3000x1400 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Example #1\n",
    "W = np.array([[3, 0], [0, 1]])\n",
    "plot_eig_vec_transform(W)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "id": "dc021f60",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 3000x1400 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Example #2\n",
    "W = np.array([[0, 1], [1, 0]])\n",
    "plot_eig_vec_transform(W)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "fbbba205",
   "metadata": {},
   "source": [
    "As we saw above, looking at how just the eigenvectors change after a transformation can be very informative about what that transformation was."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7ed6458d",
   "metadata": {},
   "source": [
    "<hr>\n",
    "\n",
    "## About this notebook\n",
    "Most of the content here is directly adapted from [Neuromatch Academy Materials](https://compneuro.neuromatch.io/tutorials/W0D3_LinearAlgebra/student/W0D3_Tutorial1.html), shared under a Creative Commons Attribution 4.0 International License."
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.9.5"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}