{ "cells": [ { "cell_type": "code", "execution_count": 8, "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": [ "# Linear Transformation " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "There are many new terminologies in this chapter, however they are not entirely new to us." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Let $V$ and $W$ be vector spaces. The mapping $T:\\ V\\rightarrow W$ is called a _linear transformation_ if an only if\n", "\n", "$$\n", "T(u+v)=T(u)+T(v)\\quad \\text{and} \\quad T(cu)=cT(u)\n", "$$\n", "\n", "for all $u,v\\in V$ and all $c\\in R$. If $T:\\ V\\rightarrow W$, then $T$ is called a _linear operator_. For each $u\\in V$, the vector $w=T(u)$ is called the _image_ of $u$ under $T$." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Parametric Function Plotting " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We need one tool for illustrating linear transformation.\n", "\n", "We want to plot any line in vector space by an equation: $p = p_0+tv $. We need to know vector $p_0$ and $v$ to plot the line. \n", "\n", "For instance, $p_0 = (2, 6)$, $v=(5, 3)$ and $p = (x, y)$, subsitute them into our equation\n", "$$\n", "\\left[\n", "\\begin{matrix}\n", "x\\\\y\n", "\\end{matrix}\n", "\\right]=\\left[\n", "\\begin{matrix}\n", "2\\\\6\n", "\\end{matrix}\n", "\\right]+\n", "t\\left[\n", "\\begin{matrix}\n", "5\\\\3\n", "\\end{matrix}\n", "\\right]\n", "$$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We will create a plot to illustrate the linear transformation later." ] }, { "cell_type": "code", "execution_count": 15, "metadata": {}, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "\n", "\n", "def paraEqPlot(p0, v0, p1, v1):\n", " t = np.linspace(-5, 5)\n", " \n", " ################### First Line ####################\n", " fig, ax = plt.subplots(figsize=(10, 10))\n", " \n", " # Plot first line\n", " x = p0[0, 0] + v0[0, 0] * t\n", " y = p0[1, 0] + v0[1, 0] * t\n", " ax.plot(x, y, lw=3, color='red')\n", " ax.grid(True)\n", " ax.scatter(p0[0, 0], p0[1, 0], s=150, edgecolor='red', facecolor='black', zorder=3)\n", " \n", " # Plot second line\n", " x = p1[0, 0] + v1[0, 0] * t\n", " y = p1[1, 0] + v1[1, 0] * t\n", " ax.plot(x, y, lw=3, color='blue')\n", " ax.grid(True)\n", " ax.scatter(p1[0, 0], p1[1, 0], s=150, edgecolor='red', facecolor='black', zorder=3)\n", " \n", " # Set the position of the spines\n", " ax.spines['left'].set_position('zero')\n", " ax.spines['bottom'].set_position('zero')\n", "\n", " # Eliminate upper and right axes\n", " ax.spines['right'].set_color('none')\n", " ax.spines['top'].set_color('none')\n", "\n", " # Show ticks in the left and lower axes only\n", " ax.xaxis.set_ticks_position('bottom')\n", " ax.yaxis.set_ticks_position('left')\n", " \n", " # Add text annotations\n", " string = f'$({int(p0[0, 0])}, {int(p0[1, 0])})$'\n", " ax.text(x=p0[0, 0] + 0.5, y=p0[1, 0], s=string, size=14)\n", " \n", " string = f'$({int(p1[0, 0])}, {int(p1[1, 0])})$'\n", " ax.text(x=p1[0, 0] + 0.5, y=p1[1, 0], s=string, size=14)\n", " \n", " plt.show()\n", "\n", "# Example usage\n", "p0 = np.array([[1], [2]])\n", "v0 = np.array([[1], [0.5]])\n", "p1 = np.array([[2], [3]])\n", "v1 = np.array([[0.5], [1]])\n", "\n", "paraEqPlot(p0, v0, p1, v1)\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## A Simple Linear Transformation " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now we know the parametric functions in $\\mathbb{R}^2$, we can show how a linear transformation acturally works on a line." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Let's say, we perform linear transformation on a vector $(x, y)$, \n", "\n", "$$\n", "T\\left(\\begin{bmatrix} x \\\\ y \\end{bmatrix}\\right) = \\begin{pmatrix} 3x - 2y \\\\ -2x + 3y \\end{pmatrix}\n", "$$\n", "and substitute the parametric function into the linear operator.\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "$$\n", "T\\left(\\begin{bmatrix} 4+t \\\\ 5+3t \\end{bmatrix}\\right) = \\begin{pmatrix} 3(4+t) - 2(5+3t) \\\\ -2(4+t) + 3(5+3t) \\end{pmatrix} = \\begin{bmatrix} 2 - 3t \\\\ 7 + 7t \\end{bmatrix}\n", "$$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The red line is transformed into blue line and point $(4, 5)$ transformed into $(2, 7)$" ] }, { "cell_type": "code", "execution_count": 16, "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "p0 = np.array([[4],[5]])\n", "v0 = np.array([[1],[3]])\n", "p1 = np.array([[2],[7]])\n", "v1 = np.array([[-3],[7]])\n", "paraEqPlot(p0,v0,p1, v1)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Visualization of Change of Basis " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Change of basis is also a kind of linear transformation. Let's create a grid." ] }, { "cell_type": "code", "execution_count": 11, "metadata": {}, "outputs": [], "source": [ "u1, u2 = np.linspace(-5, 5, 10), np.linspace(-5, 5, 10)\n", "U1, U2 = np.meshgrid(u1, u2)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We plot each row of $U2$ again each row of $U1$" ] }, { "cell_type": "code", "execution_count": 12, "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig, ax = plt.subplots(figsize = (10, 10))\n", "ax.plot(U1,U2, color = 'black') \n", "ax.plot(U1.T,U2.T, color = 'black') \n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Let $A$ and $B$ be two bases in $\\mathbb{R}^3$\n", " \n", "$$\n", "A = \\left\\{ \\begin{bmatrix} 2 \\\\ 1 \\end{bmatrix}, \\ \\begin{bmatrix} 1 \\\\ 1 \\end{bmatrix} \\right\\} \\\\\n", "B = \\left\\{ \\begin{bmatrix} 3 \\\\ 2 \\end{bmatrix}, \\ \\begin{bmatrix} 0 \\\\ -1 \\end{bmatrix} \\right\\}\n", "$$\n", "\n", "If we want to use basis $A$ to represent $B$, we can construct an augmented matrix like we did before.\n", "\n", "$$\n", "[A|B]=\n", "\\left[\n", "\\begin{matrix}\n", "2 & 1 & 3 & 0\\\\\n", "1 & 1 & 2 & -1\n", "\\end{matrix}\n", "\\right]\n", "$$" ] }, { "cell_type": "code", "execution_count": 13, "metadata": {}, "outputs": [ { "data": { "text/latex": [ "$\\displaystyle \\left( \\left[\\begin{matrix}1 & 0 & 1 & 1\\\\0 & 1 & 1 & -2\\end{matrix}\\right], \\ \\left( 0, \\ 1\\right)\\right)$" ], "text/plain": [ "⎛⎡1 0 1 1 ⎤ ⎞\n", "⎜⎢ ⎥, (0, 1)⎟\n", "⎝⎣0 1 1 -2⎦ ⎠" ] }, "execution_count": 13, "metadata": {}, "output_type": "execute_result" } ], "source": [ "AB = sy.Matrix([[2,1,3,0],[1,1,2,-1]]); AB.rref()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We find the transition matrix $P_{A\\leftarrow B}$\n", "$$\n", "[A|B]=[I|P_{A\\leftarrow B}]\n", "$$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We can write\n", "\n", "$$\n", "\\big[x\\big]_A = P_{A\\leftarrow B}\\big[u\\big]_B\\\\\n", "\\left[\n", "\\begin{matrix}\n", "x_1\\\\x_2\n", "\\end{matrix}\n", "\\right]\n", "=\n", "\\left[\n", "\\begin{matrix}\n", "1 & 1\\\\1 & -2\n", "\\end{matrix}\n", "\\right]\n", "\\left[\n", "\\begin{matrix}\n", "u_1\\\\u_2\n", "\\end{matrix}\n", "\\right]\\\\\n", "$$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Therefore\n", "$$\n", "x_1 = u_1+u_2\\\\\n", "x_2 = u_1 - 2u_2\n", "$$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Let's plot original and transformed coordinates together." ] }, { "cell_type": "code", "execution_count": 14, "metadata": {}, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "u1, u2 = np.linspace(-10, 10, 21), np.linspace(-10, 10, 21)\n", "U1, U2 = np.meshgrid(u1, u2)\n", "\n", "fig, ax = plt.subplots(figsize = (10, 10))\n", "ax.plot(U1,U2, color = 'black', lw = 1) \n", "ax.plot(U1.T,U2.T, color = 'black', lw = 1) \n", "\n", "X1 = U1 +U2\n", "X2 = U1 - 2*U2\n", "ax.plot(X1,X2, color = 'red', ls = '--') \n", "ax.plot(X1.T,X2.T, color = 'red', ls = '--') \n", "\n", "ax.arrow(0, 0, 1, 1, color = 'blue', width = .07, \n", " length_includes_head = True,\n", " head_width = .2, # default: 3*width\n", " head_length = .3, zorder = 4,\n", " overhang = .4)\n", "\n", "ax.arrow(0, 0, 1, -2, color = 'blue', width = .07, \n", " length_includes_head = True,\n", " head_width = .2, # default: 3*width\n", " head_length = .3,zorder = 4,\n", " overhang = .4)\n", "\n", "ax.text(0.1,0.1,'$(0, 0)$',size = 14)\n", "ax.scatter(0,0,s = 120, zorder = 5, ec = 'red', fc = 'black')\n", "\n", "ax.axis([-4, 4, -5, 5])\n", "plt.show()" ] } ], "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": 2 }