{ "cells": [ { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "import matplotlib.pyplot as plt\n", "import numpy as np\n", "import sympy as sy\n", "sy.init_printing() " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Null Space " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The _null space_, denoted as $\\text{Nul}A$ is the solution set of a homogeneous linear system, i.e. $Ax=0$. \n", "\n", "A null space is a always a subspace of $\\mathbb{R}^n$, why? Because one solution can always be the origin $(0, 0, ...)$.\n", "\n", "As an example, consider a linear system.\n", "\n", "$$\n", "2x_1-x_2+x_3 = 0\\\\\n", "x_1+2x_2+3x_3= 0 \n", "$$\n", "\n", "The augmented matrix is \n", "\n", "$$\n", "\\left[\n", "\\begin{matrix}\n", "2 & -1 & 1 & 0\\\\\n", "1 & 2 & 3 & 0\n", "\\end{matrix}\n", "\\right]\n", "$$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Before solving the system, we have already known there is no unique solution since a free variable presents, due to the fact that two equation with three variables.\n", "\n", "Solve for the reduced echelon form." ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [ { "data": { "text/latex": [ "$\\displaystyle \\left( \\left[\\begin{matrix}1 & 0 & 1 & 0\\\\0 & 1 & 1 & 0\\end{matrix}\\right], \\ \\left( 0, \\ 1\\right)\\right)$" ], "text/plain": [ "⎛⎡1 0 1 0⎤ ⎞\n", "⎜⎢ ⎥, (0, 1)⎟\n", "⎝⎣0 1 1 0⎦ ⎠" ] }, "execution_count": 2, "metadata": {}, "output_type": "execute_result" } ], "source": [ "Aug = sy.Matrix([[2,-1,1,0],[1,2,3,0]])\n", "Aug.rref()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "$x_3$ is a free variable, the solution set can be written as\n", "\n", "$$\n", "\\left[\n", "\\begin{matrix}\n", "x_1 \\\\ x_2 \\\\ x_3\n", "\\end{matrix}\n", "\\right]=\n", "\\left[\n", "\\begin{matrix}\n", "-x_3 \\\\ -x_3 \\\\ x_3\n", "\\end{matrix}\n", "\\right]=\n", "x_3\\left[\n", "\\begin{matrix}\n", "-1 \\\\ -1 \\\\ 1\n", "\\end{matrix}\n", "\\right]\n", "$$\n", "\n", "which is a line passing both origin $(0, 0, 0)$ and $(-1, -1, 1)$, also a subspace of $\\mathbb{R}^3$." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now consider another example, suppose we have an augmented matrix" ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [ { "data": { "text/latex": [ "$\\displaystyle \\left[\\begin{matrix}-3 & 6 & -1 & 1 & -7 & 0\\\\1 & -2 & 2 & 3 & -1 & 0\\\\2 & -4 & 5 & 8 & -4 & 0\\end{matrix}\\right]$" ], "text/plain": [ "⎡-3 6 -1 1 -7 0⎤\n", "⎢ ⎥\n", "⎢1 -2 2 3 -1 0⎥\n", "⎢ ⎥\n", "⎣2 -4 5 8 -4 0⎦" ] }, "execution_count": 3, "metadata": {}, "output_type": "execute_result" } ], "source": [ "Aug = sy.Matrix([[-3,6,-1,1,-7,0],[1,-2,2,3,-1,0],[2,-4,5,8,-4,0]]);Aug" ] }, { "cell_type": "code", "execution_count": 4, "metadata": { "scrolled": true }, "outputs": [ { "data": { "text/latex": [ "$\\displaystyle \\left( \\left[\\begin{matrix}1 & -2 & 0 & -1 & 3 & 0\\\\0 & 0 & 1 & 2 & -2 & 0\\\\0 & 0 & 0 & 0 & 0 & 0\\end{matrix}\\right], \\ \\left( 0, \\ 2\\right)\\right)$" ], "text/plain": [ "⎛⎡1 -2 0 -1 3 0⎤ ⎞\n", "⎜⎢ ⎥ ⎟\n", "⎜⎢0 0 1 2 -2 0⎥, (0, 2)⎟\n", "⎜⎢ ⎥ ⎟\n", "⎝⎣0 0 0 0 0 0⎦ ⎠" ] }, "execution_count": 4, "metadata": {}, "output_type": "execute_result" } ], "source": [ "Aug.rref()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The solution can be written as:" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "$$\n", "\\left[\n", "\\begin{matrix}\n", "x_1 \\\\ x_2 \\\\ x_3 \\\\x_4 \\\\ x_5\n", "\\end{matrix}\n", "\\right]=\n", "\\left[\n", "\\begin{matrix}\n", "2x_2+x_4-3x_5 \\\\ x_2 \\\\ -2x_4+2x_5 \\\\x_4 \\\\ x_5\n", "\\end{matrix}\n", "\\right]=\n", "x_2\\left[\n", "\\begin{matrix}\n", "2 \\\\ 1 \\\\ 0 \\\\0 \\\\ 0\n", "\\end{matrix}\n", "\\right]\n", "+\n", "x_4\\left[\n", "\\begin{matrix}\n", "1 \\\\ 0 \\\\ -2 \\\\1 \\\\ 0\n", "\\end{matrix}\n", "\\right]\n", "+x_5\\left[\n", "\\begin{matrix}\n", "-3 \\\\ 0 \\\\ 2 \\\\0 \\\\ 1\n", "\\end{matrix}\n", "\\right]\n", "$$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The $\\text{Nul}A$ is a subspace in $\\mathbb{R}^5$ with $\\text{dim}A=3$. " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Null Space vs Col Space " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Consider matrix $A$" ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [ { "data": { "text/latex": [ "$\\displaystyle \\left[\\begin{matrix}2 & 4 & -2 & 1\\\\-2 & -5 & 7 & 3\\\\3 & 7 & -8 & 6\\end{matrix}\\right]$" ], "text/plain": [ "⎡2 4 -2 1⎤\n", "⎢ ⎥\n", "⎢-2 -5 7 3⎥\n", "⎢ ⎥\n", "⎣3 7 -8 6⎦" ] }, "execution_count": 5, "metadata": {}, "output_type": "execute_result" } ], "source": [ "A = sy.Matrix([[2,4,-2,1],[-2,-5,7,3],[3,7,-8,6]]);A" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Column space is a subspace in $\\mathbb{R}^n$, what is $n$? It is the number of rows, $n=3$.\n", "\n", "Null space is a subspace in $\\mathbb{R}^m$, what is $m$? It is the number of columns, $m=4$." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "How to find any nonzero vector in $\\text{Col}A$ and in $\\text{Nul}A$?\n", "\n", "Any column in a matrix can be a nonzero vector in $\\text{Col}A$, for instance first column: $(2, -2, 3)^T$." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "But to find a nonzero vector in null space requires some effort, construct the augmented matrix then turn it into rref." ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [ { "data": { "text/latex": [ "$\\displaystyle \\left( \\left[\\begin{matrix}1 & 0 & 9 & 0 & 0\\\\0 & 1 & -5 & 0 & 0\\\\0 & 0 & 0 & 1 & 0\\end{matrix}\\right], \\ \\left( 0, \\ 1, \\ 3\\right)\\right)$" ], "text/plain": [ "⎛⎡1 0 9 0 0⎤ ⎞\n", "⎜⎢ ⎥ ⎟\n", "⎜⎢0 1 -5 0 0⎥, (0, 1, 3)⎟\n", "⎜⎢ ⎥ ⎟\n", "⎝⎣0 0 0 1 0⎦ ⎠" ] }, "execution_count": 6, "metadata": {}, "output_type": "execute_result" } ], "source": [ "Aug = sy.Matrix([[2,4,-2,1,0],[-2,-5,7,3,0],[3,7,-8,6,0]]);Aug.rref()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The solution set with a free variable $x_3$ (because column 3 has no pivot) is \n", "\n", "$$\n", "\\left[\n", "\\begin{matrix}\n", "x_1 \\\\ x_2 \\\\ x_3\\\\x_4\n", "\\end{matrix}\n", "\\right]=\n", "\\left[\n", "\\begin{matrix}\n", "-9x_3 \\\\ 5x_3 \\\\ x_3\\\\0\n", "\\end{matrix}\n", "\\right]\n", "$$\n", "\n", "If we pick $x_3 =1$, a nonzero vector in $\\text{Nul}A$ is $(-9, 5, 1, 0)^T$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now consider two vectors\n", "\n", "$$\n", "u = \\left[\n", "\\begin{matrix}\n", "3 \\\\ -2 \\\\ -1\\\\ 0 \n", "\\end{matrix}\n", "\\right],\\qquad\n", "v = \\left[\n", "\\begin{matrix}\n", "3 \\\\ -1\\\\3\n", "\\end{matrix}\n", "\\right]\\\\\n", "$$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Is $u$ in $\\text{Nul}A$? It can be verified easily" ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [ { "data": { "text/latex": [ "$\\displaystyle \\left[\\begin{matrix}0\\\\-3\\\\3\\end{matrix}\\right]$" ], "text/plain": [ "⎡0 ⎤\n", "⎢ ⎥\n", "⎢-3⎥\n", "⎢ ⎥\n", "⎣3 ⎦" ] }, "execution_count": 7, "metadata": {}, "output_type": "execute_result" } ], "source": [ "u = sy.Matrix([[3],[-2],[-1],[0]])\n", "A*u" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "$Au\\neq \\mathbf{0}$, therefore $u$ is not in $\\text{Nul}A$." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Is $v$ in $\\text{Col}A$? Construct an augmented matrix with $v$, then solve it" ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [ { "data": { "text/latex": [ "$\\displaystyle \\left( \\left[\\begin{matrix}1 & 0 & 9 & 0 & 5\\\\0 & 1 & -5 & 0 & - \\frac{30}{17}\\\\0 & 0 & 0 & 1 & \\frac{1}{17}\\end{matrix}\\right], \\ \\left( 0, \\ 1, \\ 3\\right)\\right)$" ], "text/plain": [ "⎛⎡1 0 9 0 5 ⎤ ⎞\n", "⎜⎢ ⎥ ⎟\n", "⎜⎢ -30 ⎥ ⎟\n", "⎜⎢0 1 -5 0 ────⎥, (0, 1, 3)⎟\n", "⎜⎢ 17 ⎥ ⎟\n", "⎜⎢ ⎥ ⎟\n", "⎝⎣0 0 0 1 1/17⎦ ⎠" ] }, "execution_count": 8, "metadata": {}, "output_type": "execute_result" } ], "source": [ "v = sy.Matrix([[3],[-1],[3]])\n", "A.row_join(v).rref()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The augmented matrix show there are solutions, i.e. $v$ is a linear combination of its column space basis, so $v$ is in $\\text{Col}A$." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Row Space " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The **Row space** denoted as $\\text{Row}A$, contains all linear combination of row vectors and subspace in $\\mathbb{R}^n$." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "If we perform row operations on $A$ to obtain $B$, both matrices have the same row space, because $B$'s rows are linear combinations of $A$'s. However, row operation will change the row dependence. " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## An Example " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Find the row, column and null space of " ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [ { "data": { "text/latex": [ "$\\displaystyle \\left[\\begin{matrix}-2 & -5 & 8 & 0 & -17\\\\1 & 3 & -5 & 1 & 5\\\\3 & 11 & -19 & 7 & 1\\\\1 & 7 & -13 & 5 & -3\\end{matrix}\\right]$" ], "text/plain": [ "⎡-2 -5 8 0 -17⎤\n", "⎢ ⎥\n", "⎢1 3 -5 1 5 ⎥\n", "⎢ ⎥\n", "⎢3 11 -19 7 1 ⎥\n", "⎢ ⎥\n", "⎣1 7 -13 5 -3 ⎦" ] }, "execution_count": 9, "metadata": {}, "output_type": "execute_result" } ], "source": [ "A = sy.Matrix([[-2, -5, 8, 0, -17],\n", " [1, 3, -5, 1, 5], \n", " [3, 11, -19, 7, 1], \n", " [1, 7, -13, 5, -3]]);A" ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [ { "data": { "text/latex": [ "$\\displaystyle \\left( \\left[\\begin{matrix}1 & 0 & 1 & 0 & 1\\\\0 & 1 & -2 & 0 & 3\\\\0 & 0 & 0 & 1 & -5\\\\0 & 0 & 0 & 0 & 0\\end{matrix}\\right], \\ \\left( 0, \\ 1, \\ 3\\right)\\right)$" ], "text/plain": [ "⎛⎡1 0 1 0 1 ⎤ ⎞\n", "⎜⎢ ⎥ ⎟\n", "⎜⎢0 1 -2 0 3 ⎥ ⎟\n", "⎜⎢ ⎥, (0, 1, 3)⎟\n", "⎜⎢0 0 0 1 -5⎥ ⎟\n", "⎜⎢ ⎥ ⎟\n", "⎝⎣0 0 0 0 0 ⎦ ⎠" ] }, "execution_count": 10, "metadata": {}, "output_type": "execute_result" } ], "source": [ "B = A.rref();B" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The basis of the row space of $B$ is its first 3 rows: $(1,0,1,0,1), (0, 1, -2, 0, 3), (0, 0, 0, 1, -5)$ which are also the basis of the row space of $A$. However it does not necessarily mean that first 3 rows of $A$ forms the basis for row space, because the dependence among rows changed by row operation." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "In constrast, the basis of col space of $A$ is $(-2, 1, 3, 1)^T, (-5, 3, 11, 7)^T, (0, 1, 7, 5)^T$." ] }, { "cell_type": "code", "execution_count": 11, "metadata": {}, "outputs": [ { "data": { "text/latex": [ "$\\displaystyle \\left( \\left[\\begin{matrix}1 & 0 & 1 & 0 & 1 & 0\\\\0 & 1 & -2 & 0 & 3 & 0\\\\0 & 0 & 0 & 1 & -5 & 0\\\\0 & 0 & 0 & 0 & 0 & 0\\end{matrix}\\right], \\ \\left( 0, \\ 1, \\ 3\\right)\\right)$" ], "text/plain": [ "⎛⎡1 0 1 0 1 0⎤ ⎞\n", "⎜⎢ ⎥ ⎟\n", "⎜⎢0 1 -2 0 3 0⎥ ⎟\n", "⎜⎢ ⎥, (0, 1, 3)⎟\n", "⎜⎢0 0 0 1 -5 0⎥ ⎟\n", "⎜⎢ ⎥ ⎟\n", "⎝⎣0 0 0 0 0 0⎦ ⎠" ] }, "execution_count": 11, "metadata": {}, "output_type": "execute_result" } ], "source": [ "Aug = A.row_join(sy.zeros(4,1));Aug.rref()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The null space is \n", "\n", "$$\n", "\\left[\n", "\\begin{matrix}\n", "x_1 \\\\ x_2 \\\\ x_3\\\\x_4 \\\\x_5\n", "\\end{matrix}\n", "\\right]=\n", "\\left[\n", "\\begin{matrix}\n", "-x_3-x_5 \\\\ 2x_3-3x_5 \\\\ x_3\\\\5x_5 \\\\x_5\n", "\\end{matrix}\n", "\\right]=\n", "x_3\\left[\n", "\\begin{matrix}\n", "-1 \\\\ 2 \\\\ 1\\\\0 \\\\0\n", "\\end{matrix}\n", "\\right]+\n", "x_5\n", "\\left[\n", "\\begin{matrix}\n", "-1 \\\\ -3 \\\\ 0\\\\5 \\\\1\n", "\\end{matrix}\n", "\\right]\n", "$$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Rank " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Definition of rank:\n", "The _rank_ is the dimension of the column space of $A$. The _nullity_ of $A$ is the dimension of the null space." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## The Rank Theorem" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The dimensions of the column space and the row space of an $m \\times n$ matrix $A$ are equal. Therefore, the rank is the same for either column space and row space.\n", "\n", "This common dimension, the rank of $A$, also equals the number of pivot positions in $A$ and satisfies the equation:\n", "$$\n", "\\operatorname{rank} A + \\operatorname{dim} \\mathrm{Nul} A = n\n", "$$\n", "\n", "The intuition behind this is that when a matrix $A$ is converted into its reduced row echelon form (rref) $B$, we can indirectly determine the basis of the column space by matching the columns of $B$ with those of $A$. The columns in $A$ that correspond to pivot columns in $B$ form the basis of the column space.\n", "\n", "In the rref, we can also directly see the basis of the row space. Each row in the basis of the row space must contain a pivot. The rows that do not contain pivots correspond to the free variables, which determine the dimension of the null space." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Example 1 " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "If $A$ is $45 \\times 50$ matrix with a $10$-dimension nullity, what is the rank of $A$?" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "$10$-$D$ nullity means 10 free variables, so the pivots are $50-10=40$, which is also the rank of $A$." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Example 2 " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The matrices below are row equivalent.\n", "$$\n", "A=\\left[\\begin{array}{rrrrr}\n", "2 & -1 & 1 & -6 & 8 \\\\\n", "1 & -2 & -4 & 3 & -2 \\\\\n", "-7 & 8 & 10 & 3 & -10 \\\\\n", "4 & -5 & -7 & 0 & 4\n", "\\end{array}\\right], \\quad B=\\left[\\begin{array}{rrrrr}\n", "1 & -2 & -4 & 3 & -2 \\\\\n", "0 & 3 & 9 & -12 & 12 \\\\\n", "0 & 0 & 0 & 0 & 0 \\\\\n", "0 & 0 & 0 & 0 & 0\n", "\\end{array}\\right]\n", "$$\n", "1. Find rank $A$ and $\\operatorname{dim}$ Nul $A$\n", "2. Find bases for Col $A$ and Row $A$.\n", "3. What is the next step to perform to find a basis for Nul $A$ ?\n", "4. How many pivot columns are in a row echelon form of $A^{T} ?$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "1. $rank(A)=2$, because $B$ has two pivots. And nullity is the number of free variables, there are 3, so $\\text{dim Nul}A = 3$. " ] }, { "cell_type": "code", "execution_count": 12, "metadata": {}, "outputs": [ { "data": { "text/latex": [ "$\\displaystyle \\left( \\left[\\begin{matrix}1 & 0 & 2 & -5 & 6 & 0\\\\0 & 1 & 3 & -4 & 4 & 0\\\\0 & 0 & 0 & 0 & 0 & 0\\\\0 & 0 & 0 & 0 & 0 & 0\\end{matrix}\\right], \\ \\left( 0, \\ 1\\right)\\right)$" ], "text/plain": [ "⎛⎡1 0 2 -5 6 0⎤ ⎞\n", "⎜⎢ ⎥ ⎟\n", "⎜⎢0 1 3 -4 4 0⎥ ⎟\n", "⎜⎢ ⎥, (0, 1)⎟\n", "⎜⎢0 0 0 0 0 0⎥ ⎟\n", "⎜⎢ ⎥ ⎟\n", "⎝⎣0 0 0 0 0 0⎦ ⎠" ] }, "execution_count": 12, "metadata": {}, "output_type": "execute_result" } ], "source": [ "A = sy.Matrix([[2,-1,1,-6,8,0],\n", " [1,-2,-4,3,-2,0],\n", " [-7,8,10,3,-10,0],\n", " [4,-5,-7,0,4,0]])\n", "A.rref()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "2. Bases for $\\text{Col}A$ is $(2,1,-7,4)^T, (-1,-2,8,-5)^T$, and for $\\text{Row}A$ is $(1,-2,-4,3,-2),(0,3,9,-12,12)$." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The $\\text{Nul}A$ and basis is\n", "\n", "$$\n", "\\left[\n", "\\begin{matrix}\n", "x_1 \\\\ x_2 \\\\ x_3\\\\x_4 \\\\x_5\n", "\\end{matrix}\n", "\\right]=\n", "\\left[\n", "\\begin{matrix}\n", "-2x_3+5x_4-6x_5 \\\\ -3x_3+4x_4-4x_5 \\\\ x_3\\\\x_4 \\\\x_5\n", "\\end{matrix}\n", "\\right]=\n", "x_3\n", "\\left[\n", "\\begin{matrix}\n", "-2 \\\\ -3 \\\\ 1\\\\0 \\\\0\n", "\\end{matrix}\n", "\\right]+\n", "x_4\n", "\\left[\n", "\\begin{matrix}\n", "5 \\\\ 4 \\\\ 0\\\\1 \\\\0\n", "\\end{matrix}\n", "\\right]+\n", "x_5\n", "\\left[\n", "\\begin{matrix}\n", "-6 \\\\ -4 \\\\ 0\\\\0 \\\\1\n", "\\end{matrix}\n", "\\right]\n", "$$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "3. Perform rref on augmented $A$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "4. Transpose $A$ then do rref." ] }, { "cell_type": "code", "execution_count": 13, "metadata": {}, "outputs": [ { "data": { "text/latex": [ "$\\displaystyle \\left( \\left[\\begin{matrix}1 & 0 & -2 & 1\\\\0 & 1 & -3 & 2\\\\0 & 0 & 0 & 0\\\\0 & 0 & 0 & 0\\\\0 & 0 & 0 & 0\\\\0 & 0 & 0 & 0\\end{matrix}\\right], \\ \\left( 0, \\ 1\\right)\\right)$" ], "text/plain": [ "⎛⎡1 0 -2 1⎤ ⎞\n", "⎜⎢ ⎥ ⎟\n", "⎜⎢0 1 -3 2⎥ ⎟\n", "⎜⎢ ⎥ ⎟\n", "⎜⎢0 0 0 0⎥ ⎟\n", "⎜⎢ ⎥, (0, 1)⎟\n", "⎜⎢0 0 0 0⎥ ⎟\n", "⎜⎢ ⎥ ⎟\n", "⎜⎢0 0 0 0⎥ ⎟\n", "⎜⎢ ⎥ ⎟\n", "⎝⎣0 0 0 0⎦ ⎠" ] }, "execution_count": 13, "metadata": {}, "output_type": "execute_result" } ], "source": [ "A.T.rref()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "There are 2 pivot columns." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Actually, we don't need any calculation to know the rank of $A^T$, because\n", "\n", "$$\n", "rank(A)=rank(A^T)\n", "$$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Orthogonality of $\\text{Nul}A$ and $\\text{Row}A$ " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## $\\text{Nul}A \\perp \\text{Row}A$ " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Here is the intersting connections of these subspaces we have discussed. Consider" ] }, { "cell_type": "code", "execution_count": 14, "metadata": {}, "outputs": [ { "data": { "text/latex": [ "$\\displaystyle \\left[\\begin{matrix}5 & 8 & 2\\\\10 & 16 & 4\\\\3 & 4 & 1\\end{matrix}\\right]$" ], "text/plain": [ "⎡5 8 2⎤\n", "⎢ ⎥\n", "⎢10 16 4⎥\n", "⎢ ⎥\n", "⎣3 4 1⎦" ] }, "execution_count": 14, "metadata": {}, "output_type": "execute_result" } ], "source": [ "A = sy.Matrix([[5, 8, 2], [10, 16, 4], [3, 4, 1]]);A" ] }, { "cell_type": "code", "execution_count": 15, "metadata": {}, "outputs": [ { "data": { "text/latex": [ "$\\displaystyle \\left( \\left[\\begin{matrix}1 & 0 & 0\\\\0 & 1 & \\frac{1}{4}\\\\0 & 0 & 0\\end{matrix}\\right], \\ \\left( 0, \\ 1\\right)\\right)$" ], "text/plain": [ "⎛⎡1 0 0 ⎤ ⎞\n", "⎜⎢ ⎥ ⎟\n", "⎜⎢0 1 1/4⎥, (0, 1)⎟\n", "⎜⎢ ⎥ ⎟\n", "⎝⎣0 0 0 ⎦ ⎠" ] }, "execution_count": 15, "metadata": {}, "output_type": "execute_result" } ], "source": [ "A.rref()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The basis of row space of $A$ is $(1, 0, 0)$ and $(0, 1, .25)$.And the $\\text{Row}A$ is \n", "\n", "$$\n", "\\text{Row}A=\n", "s\\left[\n", "\\begin{matrix}\n", "1 \\\\ 0\\\\ 0\n", "\\end{matrix}\n", "\\right]+\n", "t\\left[\n", "\\begin{matrix}\n", "0 \\\\ 1\\\\ 0.25\n", "\\end{matrix}\n", "\\right]\n", "$$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The $\\text{Nul}A$ is \n", "$$\n", "\\left[\n", "\\begin{matrix}\n", "x_1 \\\\ x_2\\\\ x_3\n", "\\end{matrix}\n", "\\right]=\n", "x_3\n", "\\left[\n", "\\begin{matrix}\n", "0 \\\\ -.25\\\\ 1\n", "\\end{matrix}\n", "\\right]\n", "$$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now we can visualize their relations geometrically. Again keep in mind that Matplotlib does not render 3D properly, so you need some imagination as well.\n", "\n", "Here is what we observe. \n", "\n", "The $\\text{Row}A$ is a plane and $\\text{Nul}A$ is a line which is perpendicular to the plane (maybe 3D plot not so obvious about it). It is easy to grasp the idea if you notice that in a homogeneous system $Ab = \\mathbf{0}$, it breaks down into dot products\n", "\n", "$$\n", "Ab =\\left[\n", "\\begin{matrix}\n", "A_{1\\cdot}\\cdot b \\\\ A_{2\\cdot}\\cdot b\\\\ A_{3\\cdot}\\cdot b \n", "\\end{matrix}\n", "\\right] \n", "=\n", "\\left[\n", "\\begin{matrix}\n", "0 \\\\ 0 \\\\ 0\n", "\\end{matrix}\n", "\\right] \n", "$$\n", "\n", "where $A_{1\\cdot}, A_{2\\cdot}, A_{3\\cdot}$ are the rows of $A$. In later chapters we will prove when the dot product of two vectors equals zero, they are geometrically perpendicular." ] }, { "cell_type": "code", "execution_count": 17, "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "\n", "# Generate the grid\n", "s = np.linspace(-1, 1, 10)\n", "t = np.linspace(-1, 1, 10)\n", "S, T = np.meshgrid(s, t)\n", "\n", "X = S\n", "Y = T\n", "Z = T * 0.25\n", "\n", "# Create the figure and the 3D axis\n", "fig = plt.figure(figsize=(8, 8))\n", "ax = fig.add_subplot(111, projection='3d')\n", "\n", "# Plot the surface\n", "ax.plot_surface(X, Y, Z, alpha=0.9, cmap=plt.cm.coolwarm)\n", "\n", "# Plot the line\n", "x3 = np.linspace(-1, 1, 10)\n", "x1 = 0 * x3\n", "x2 = -0.25 * x3\n", "ax.plot(x1, x2, x3, lw=5)\n", "\n", "# Set axis labels\n", "ax.set_xlabel('x-axis', size=18)\n", "ax.set_ylabel('y-axis', size=18)\n", "ax.set_zlabel('z-axis', size=18)\n", "\n", "# Set axis limits\n", "ax.set_xlim([-1, 1])\n", "ax.set_ylim([-1, 1])\n", "ax.set_zlim([-0.25, 0.25])\n", "\n", "# Add text annotations\n", "ax.text(1, -1, -0.25, r'$Row\\ A$', size=17)\n", "ax.text(0, -0.25, 1, r'$Nul\\ A$', size=17)\n", "\n", "# Set the view angle\n", "ax.view_init(elev=7, azim=20)\n", "\n", "# Show the plot\n", "plt.show()\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Let me write a summary:\n", "1. The dimension of the row space is equal to the dimension of the column space (both are the rank of the matrix).\n", "2. The row space of $A$ is orthogonal to the null space of $A$.\n", "3. The column space of $A$ is orthogonal to the left null space of $A$." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## $\\text{Nul}A^T \\perp \\text{Col}A$ " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The nullity of $A^T$ is" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [ { "data": { "image/png": "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", "text/latex": [ "$\\displaystyle \\left( \\left[\\begin{matrix}1 & 2 & 0\\\\0 & 0 & 1\\\\0 & 0 & 0\\end{matrix}\\right], \\ \\left( 0, \\ 2\\right)\\right)$" ], "text/plain": [ "⎛⎡1 2 0⎤ ⎞\n", "⎜⎢ ⎥ ⎟\n", "⎜⎢0 0 1⎥, (0, 2)⎟\n", "⎜⎢ ⎥ ⎟\n", "⎝⎣0 0 0⎦ ⎠" ] }, "execution_count": 58, "metadata": {}, "output_type": "execute_result" } ], "source": [ "A = sy.Matrix([[5, 8, 2], [10, 16, 4], [3, 4, 1]]);A.T.rref()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The $\\text{Nul}A^T$ is \n", "\n", "$$\n", "\\left[\n", "\\begin{matrix}\n", "x_1 \\\\ x_2\\\\ x_3\n", "\\end{matrix}\n", "\\right]=\n", "x_2\n", "\\left[\n", "\\begin{matrix}\n", "-2 \\\\ 1\\\\ 0\n", "\\end{matrix}\n", "\\right]\n", "$$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The $\\text{Col}A$ is " ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [ { "data": { "image/png": "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", "text/latex": [ "$\\displaystyle \\left( \\left[\\begin{matrix}1 & 0 & 0\\\\0 & 1 & \\frac{1}{4}\\\\0 & 0 & 0\\end{matrix}\\right], \\ \\left( 0, \\ 1\\right)\\right)$" ], "text/plain": [ "⎛⎡1 0 0 ⎤ ⎞\n", "⎜⎢ ⎥ ⎟\n", "⎜⎢0 1 1/4⎥, (0, 1)⎟\n", "⎜⎢ ⎥ ⎟\n", "⎝⎣0 0 0 ⎦ ⎠" ] }, "execution_count": 43, "metadata": {}, "output_type": "execute_result" } ], "source": [ "A.rref()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "$$\n", "\\text{Col}A=\n", "s\\left[\n", "\\begin{matrix}\n", "5 \\\\ 10\\\\ 3\n", "\\end{matrix}\n", "\\right]+\n", "t\\left[\n", "\\begin{matrix}\n", "8 \\\\ 16\\\\ 4\n", "\\end{matrix}\n", "\\right]\n", "$$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "$\\text{Col}A$ is a plane and $\\text{Nul}A^T$ is a line perpendicular to the plane. The intuition is similar to $\\text{Nul}A \\perp \\text{Row}A$, here you can think of a system look like $b^TA = \\mathbf{0}^T$." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "%matplotlib inline\n", "s = np.linspace(-1, 1, 10)\n", "t = np.linspace(-1, 1, 10)\n", "S, T = np.meshgrid(s, t)\n", "\n", "X = 5*S+8*T\n", "Y = 10*S+16*T\n", "Z = 3*S+4*T\n", "\n", "fig = plt.figure(figsize = (8,8))\n", "\n", "ax = fig.add_subplot(111,projection='3d')\n", "ax.plot_surface(X, Y, Z, cmap=plt.cm.coolwarm)\n", "\n", "x2 = np.linspace(-1, 1, 10)\n", "x3 = x2*0\n", "x1 = -2*x2\n", "\n", "ax.plot(x1,x2,x3, lw = 3)\n", "\n", "ax.set_xlabel('x-axis', size = 18)\n", "ax.set_ylabel('y-axis', size = 18)\n", "ax.set_zlabel('z-axis', size = 18)\n", "\n", "ax.axis([-1,1,-1,1])\n", "\n", "ax.view_init(-67, 35)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Rank Decomposition " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Consider a matrix $A$, the purpose is to decompose it into the multiplication of $C$, $R$, which are the bases of column space and row space respectively." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "$$\n", "A = CR\n", "$$" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [ { "data": { "image/png": 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"text/latex": [ "$\\displaystyle \\left[\\begin{matrix}2 & 4 & 1 & -1\\\\4 & 2 & -4 & 2\\\\2 & -2 & -5 & 3\\\\1 & 9 & -3 & 2\\end{matrix}\\right]$" ], "text/plain": [ "⎡2 4 1 -1⎤\n", "⎢ ⎥\n", "⎢4 2 -4 2 ⎥\n", "⎢ ⎥\n", "⎢2 -2 -5 3 ⎥\n", "⎢ ⎥\n", "⎣1 9 -3 2 ⎦" ] }, "execution_count": 61, "metadata": {}, "output_type": "execute_result" } ], "source": [ "A = sy.Matrix([[2, 4, 1, -1], [4, 2, -4, 2], [2, -2, -5, 3], [1, 9, -3, 2]]);A" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/latex": [ "$\\displaystyle \\left( \\left[\\begin{matrix}1 & 0 & 0 & - \\frac{4}{21}\\\\0 & 1 & 0 & \\frac{1}{63}\\\\0 & 0 & 1 & - \\frac{43}{63}\\\\0 & 0 & 0 & 0\\end{matrix}\\right], \\ \\left( 0, \\ 1, \\ 2\\right)\\right)$" ], "text/plain": [ "⎛⎡1 0 0 -4/21⎤ ⎞\n", "⎜⎢ ⎥ ⎟\n", "⎜⎢0 1 0 1/63 ⎥ ⎟\n", "⎜⎢ ⎥ ⎟\n", "⎜⎢ -43 ⎥, (0, 1, 2)⎟\n", "⎜⎢0 0 1 ──── ⎥ ⎟\n", "⎜⎢ 63 ⎥ ⎟\n", "⎜⎢ ⎥ ⎟\n", "⎝⎣0 0 0 0 ⎦ ⎠" ] }, "execution_count": 62, "metadata": {}, "output_type": "execute_result" } ], "source": [ "Arref = A.rref();Arref" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Get the basis of $\\text{Col}A$." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [ { "data": { "image/png": "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", "text/latex": [ "$\\displaystyle \\left[\\begin{matrix}2 & 4 & 1\\\\4 & 2 & -4\\\\2 & -2 & -5\\\\1 & 9 & -3\\end{matrix}\\right]$" ], "text/plain": [ "⎡2 4 1 ⎤\n", "⎢ ⎥\n", "⎢4 2 -4⎥\n", "⎢ ⎥\n", "⎢2 -2 -5⎥\n", "⎢ ⎥\n", "⎣1 9 -3⎦" ] }, "execution_count": 64, "metadata": {}, "output_type": "execute_result" } ], "source": [ "ColA_basis = A[:,:3];ColA_basis" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Then get the $\\text{Row}A$." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [ { "data": { "image/png": "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", "text/latex": [ "$\\displaystyle \\left[\\begin{matrix}1 & 0 & 0 & - \\frac{4}{21}\\\\0 & 1 & 0 & \\frac{1}{63}\\\\0 & 0 & 1 & - \\frac{43}{63}\\end{matrix}\\right]$" ], "text/plain": [ "⎡1 0 0 -4/21⎤\n", "⎢ ⎥\n", "⎢0 1 0 1/63 ⎥\n", "⎢ ⎥\n", "⎢ -43 ⎥\n", "⎢0 0 1 ──── ⎥\n", "⎣ 63 ⎦" ] }, "execution_count": 48, "metadata": {}, "output_type": "execute_result" } ], "source": [ "RowA_basis = Arref[0][0:3,:];RowA_basis" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Multiply $CR$, we are getting back $A$." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [ { "data": { "image/png": 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"text/latex": [ "$\\displaystyle \\left[\\begin{matrix}2 & 4 & 1 & -1\\\\4 & 2 & -4 & 2\\\\2 & -2 & -5 & 3\\\\1 & 9 & -3 & 2\\end{matrix}\\right]$" ], "text/plain": [ "⎡2 4 1 -1⎤\n", "⎢ ⎥\n", "⎢4 2 -4 2 ⎥\n", "⎢ ⎥\n", "⎢2 -2 -5 3 ⎥\n", "⎢ ⎥\n", "⎣1 9 -3 2 ⎦" ] }, "execution_count": 49, "metadata": {}, "output_type": "execute_result" } ], "source": [ "ColA_basis*RowA_basis" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Verify if $CR$ equals $A$." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "True" ] }, "execution_count": 50, "metadata": {}, "output_type": "execute_result" } ], "source": [ "ColA_basis*RowA_basis == A" ] } ], "metadata": { "kernelspec": { "display_name": "Python 3", "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": "3.12.4" }, "toc": { "base_numbering": 1, "nav_menu": {}, "number_sections": true, "sideBar": true, "skip_h1_title": false, "title_cell": "Table of Contents", "title_sidebar": "Contents", "toc_cell": false, "toc_position": {}, "toc_section_display": true, "toc_window_display": false } }, "nbformat": 4, "nbformat_minor": 4 }