{ "cells": [ { "cell_type": "code", "execution_count": 11, "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": [ "# Definition of Linear Independence" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "If all $c$'s are zero, a set of vectors $\\{v_1, v_2,...,v_p\\}$ is said to be _linearly independent_, if the equation\n", "\n", "$$c_{1} {v}_{1}+c_{2} {v}_{2}+\\cdots+c_{p} {v}_{p}=\\mathbf{0}$$\n", "\n", "holds.\n", "\n", "If any of $c_i\\neq 0$, the set of vectors is linearly dependent." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Example 1" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Determine if ${v}_1, {v}_2, {v}_3$ are linearly independent.\n", "$$\n", "{v}_{1}=\\left[\\begin{array}{l}\n", "1 \\\\\n", "2 \\\\\n", "3\n", "\\end{array}\\right]^T, \n", "{v}_{2}=\\left[\\begin{array}{l}\n", "4 \\\\\n", "5 \\\\\n", "6\n", "\\end{array}\\right]^T, \\text { and } {v}_{3}=\\left[\\begin{array}{l}\n", "2 \\\\\n", "1 \\\\\n", "0\n", "\\end{array}\\right]^T\n", "$$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The common way of testing linear combination is to construct augmented matrix and calculate the reduced form, for example" ] }, { "cell_type": "code", "execution_count": 12, "metadata": {}, "outputs": [ { "data": { "text/latex": [ "$\\displaystyle \\left( \\left[\\begin{matrix}1 & 0 & -2 & 0\\\\0 & 1 & 1 & 0\\\\0 & 0 & 0 & 0\\end{matrix}\\right], \\ \\left( 0, \\ 1\\right)\\right)$" ], "text/plain": [ "⎛⎡1 0 -2 0⎤ ⎞\n", "⎜⎢ ⎥ ⎟\n", "⎜⎢0 1 1 0⎥, (0, 1)⎟\n", "⎜⎢ ⎥ ⎟\n", "⎝⎣0 0 0 0⎦ ⎠" ] }, "execution_count": 12, "metadata": {}, "output_type": "execute_result" } ], "source": [ "A = sy.Matrix([[1,4,2,0],\n", " [2,5,1,0],\n", " [3,6,0,0]])\n", "A.rref()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The solution tells that $x_3$ is a free variable, so naturally it could be nonzero because $x_3\\cdot 0 =0$, therefore the set is linearly dependent." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Example 2" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Consider a matrix $A$,determine if columns of $A$ are linearly independent.\n", "\n", "$$\n", "A=\\left[\\begin{array}{rrr}\n", "0 & 1 & 4 \\\\\n", "1 & 2 & -1 \\\\\n", "5 & 8 & 0\n", "\\end{array}\\right]\n", "$$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Solve the system via augmented matrix." ] }, { "cell_type": "code", "execution_count": 13, "metadata": {}, "outputs": [ { "data": { "text/latex": [ "$\\displaystyle \\left( \\left[\\begin{matrix}1 & 0 & 0 & 0\\\\0 & 1 & 0 & 0\\\\0 & 0 & 1 & 0\\end{matrix}\\right], \\ \\left( 0, \\ 1, \\ 2\\right)\\right)$" ], "text/plain": [ "⎛⎡1 0 0 0⎤ ⎞\n", "⎜⎢ ⎥ ⎟\n", "⎜⎢0 1 0 0⎥, (0, 1, 2)⎟\n", "⎜⎢ ⎥ ⎟\n", "⎝⎣0 0 1 0⎦ ⎠" ] }, "execution_count": 13, "metadata": {}, "output_type": "execute_result" } ], "source": [ "A = sy.Matrix([[0,1,4,0],[1,2,-1,0],[5,8,0,0]])\n", "A.rref()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "$Ax=0$ has only trivial solution, i.e. $(c_1, c_2, c_3)^T = (0, 0, 0)$, so the columns of $A$ are linearly independent." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Linear independence is closly connected with linear combination, in next section we visualize the linear independence." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Visualization of Linear Independence" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "This is a visual example in $\\mathbb{R}^2$, showing $(3, 2)^T$, $(-9, -6)^T$, $(6, 4)^T$ are linearly dependent." ] }, { "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": [ "fig, ax = plt.subplots(figsize = (8, 8))\n", "#######################Arrows#######################\n", "arrows = np.array([[[0,0,3,2]],\n", " [[0,0,-9,-6]], \n", " [[0,0,6,4]]])\n", "colors = ['r','b','g']\n", "for i in range(arrows.shape[0]):\n", " X,Y,U,V = zip(*arrows[i,:,:])\n", " ax.arrow(X[0], Y[0], U[0],V[0], color = colors[i], width = .18, \n", " length_includes_head = True,\n", " head_width = .3, # default: 3*width\n", " head_length = .6,\n", " overhang = .4, zorder = -i)\n", "\n", "ax.scatter(0, 0, ec = 'red', fc = 'black', zorder = 5)\n", "ax.text(6, 4, '$(6, 4)$')\n", "ax.text(-9, -6.5, '$(-9, -6)$')\n", "ax.text(3, 2, '$(3, 2)$')\n", "\n", "ax.grid(True)\n", "ax.set_title('Linear Dependence Visualization')\n", "ax.axis([-10, 10, -10, 10])\n", "ax.set_xlabel('x-axis', size = 18)\n", "ax.set_ylabel('y-axis', size = 18)\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Simply put, _if one vector is the scalar multiple of the other vector, e.g. $3u = v$, these two vectors are linearly dependent_." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Next, we visualize linear independence in $\\mathbb{R}^3$ with vectors $(1,-2,1)^T$, $(2,1,2)^T$, $(-1,2,3)^T$." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The standard procedure is to write down the span of first two vectors, which is a plane. Then we examine whether the third vector is in the plane. If not, this set of vectors is linearly independent.\n", "\n", "$$\n", "\\left[\n", "\\begin{matrix}\n", "x\\\\\n", "y\\\\\n", "z\n", "\\end{matrix}\n", "\\right]=\n", "s\\left[\n", "\\begin{matrix}\n", "1\\\\\n", "-2\\\\\n", "1\n", "\\end{matrix}\n", "\\right]+\n", "t\\left[\n", "\\begin{matrix}\n", "2\\\\\n", "1\\\\\n", "2\n", "\\end{matrix}\n", "\\right]=\n", "\\left[\n", "\\begin{matrix}\n", "s+2t\\\\\n", "-2s+t\\\\\n", "s+2t\n", "\\end{matrix}\n", "\\right]\n", "$$" ] }, { "cell_type": "code", "execution_count": 15, "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# %matplotlib notebook, use this only when you are in Jupyter Notebook, it doesn't work in Jupyterlab\n", "fig = plt.figure(figsize = (10,10))\n", "ax = fig.add_subplot(projection='3d')\n", "\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+2*T\n", "Y = -2*S+T\n", "Z = S+2*T\n", "ax.plot_wireframe(X, Y, Z, linewidth = 1.5, color = 'k', alpha = .6)\n", "\n", "vec = np.array([[[0, 0, 0, 1, -2, 1]],\n", " [[0, 0, 0, 2, 1, 2]],\n", " [[0, 0, 0, -1, 2, 3]]])\n", "colors = ['r','b','g']\n", "for i in range(vec.shape[0]):\n", " X, Y, Z, U, V, W = zip(*vec[i,:,:])\n", " ax.quiver(X, Y, Z, U, V, W, length=1, normalize=False, color = colors[i],\n", " arrow_length_ratio = .08, pivot = 'tail',\n", " linestyles = 'solid',linewidths = 3, alpha = .6)\n", "\n", "ax.set_title('Linear Independence Visualization')\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.view_init(elev=50., azim=0)\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Pan around the image (either by setting ```ax.view_init``` or using JupyterLab widget), we can see that the green vector is not in the plane spanned by red and blue vector, thus they are linearly independent." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "
\n", "\n", "A Sidenote About Linear Independence

\n", "Let $S = \\{{v}_1,{v}_2,{v}_3, ..., {v}_n\\}$ be a set of vectors in $\\mathbb{R}^m$, if $n>m$, then $S$ is always linearly dependent. Simple example is $4$ vectors in $\\mathbb{R}^3$, even if $3$ of them are linearly independent, the $4$-th one can never be independent of them.

\n", "\n", "\n", "Also if $S = \\{{v}_1,{v}_2,{v}_3, ..., {v}_n\\}$ contains a zero vector, then the set is always linearly dependent.\n", "
" ] } ], "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 }