From 40064d644bcbbc2ee71f4c4bb18cc3d48d4d751c Mon Sep 17 00:00:00 2001 From: yenru0 Date: Wed, 24 Sep 2025 17:18:35 +0900 Subject: [PATCH] update 9.24 --- 1.ipynb => notes/1.ipynb | 0 notes/2.ipynb | 137 +++++++++++++++++++++++++++++++++++++ pdf/L2_LinearEquation0.pdf | Bin 0 -> 5164209 bytes pdf/L2_LinearEquation1.pdf | Bin 0 -> 3782331 bytes 4 files changed, 137 insertions(+) rename 1.ipynb => notes/1.ipynb (100%) create mode 100644 notes/2.ipynb create mode 100644 pdf/L2_LinearEquation0.pdf create mode 100644 pdf/L2_LinearEquation1.pdf diff --git a/1.ipynb b/notes/1.ipynb similarity index 100% rename from 1.ipynb rename to notes/1.ipynb diff --git a/notes/2.ipynb b/notes/2.ipynb new file mode 100644 index 0000000..eae2e2e --- /dev/null +++ b/notes/2.ipynb @@ -0,0 +1,137 @@ +{ + "cells": [ + { + "cell_type": "code", + "execution_count": 4, + "id": "7fc797ce", + "metadata": {}, + "outputs": [], + "source": [ + "import numpy as np\n", + "import matplotlib.pyplot as plt\n", + "\n", + "plt.rcParams[\"font.family\"] = \"D2Coding\"" + ] + }, + { + "cell_type": "markdown", + "id": "a869c82a", + "metadata": {}, + "source": [ + "# Linear Equation\n", + "\n", + "$$A\\cdot x = b$$\n", + "\n", + "* $A$: [m, n]\n", + "* $b$: [m, 1]" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "3bed3d44", + "metadata": {}, + "outputs": [], + "source": [] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "a5239ed9", + "metadata": {}, + "outputs": [], + "source": [] + }, + { + "cell_type": "markdown", + "id": "8bd218a8", + "metadata": {}, + "source": [ + "# SVD(Singular Value Decomposition)\n", + "\n", + "**why?**\n", + "\n", + "**what?**\n", + "\n", + "$$A = UWV^T$$\n", + "\n", + "* $U$: [m, n]\n", + "* $W$: [n, n] diagonal with positive or zero\n", + "* $V$: [n, n] orthogonal\n", + "\n", + "\n", + "**properties**\n", + "\n", + "* orthonormality\n", + "* uniqueness" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "563d7aec", + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "(4, 3)\n" + ] + }, + { + "data": { + "text/plain": [ + "array([[ 1., 0., -0.],\n", + " [ 1., 1., -1.],\n", + " [ 0., 1., -1.],\n", + " [-1., 1., 1.]])" + ] + }, + "execution_count": 26, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "A = np.array([[1, 0, 0], [1, 1, -1], [0, 1, -1], [-1, 1, 1]])\n", + "print(A.shape)\n", + "U, S, Vh = np.linalg.svd(A, False)" + ] + }, + { + "cell_type": "markdown", + "id": "fb89ad74", + "metadata": {}, + "source": [ + "## Homogeneous\n", + "\n", + "\n", + "## Nonhomogeneous\n", + "\n", + "\n" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "2025-02-Numerical (3.12.11)", + "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": "3.12.11" + } + }, + "nbformat": 4, + "nbformat_minor": 5 +} diff --git a/pdf/L2_LinearEquation0.pdf b/pdf/L2_LinearEquation0.pdf new file mode 100644 index 0000000000000000000000000000000000000000..65806577ceff52a53d844956ea9b80f6197b64fa GIT binary patch literal 5164209 zcmeFYWmHvP^frpLgwh>{k`U?c?hZle?(UH8?hfg06bS+8?pC@{B&72$^!LB_ea9Vl z+%NazW$4&vpS{=KYt1$1GoKlUN=Z!O4Ko8LDiYNv@P~@T3}J%U8Cs$u@$oULdDxpU ziW)c@SlgK~DjArWI6+vzWfev_16wm16I)scqpGu`i;=UMqlt-%ot-m;mE+$HiZ0I9 z7PjDiR%WihBjgPnt)y*D?Z8u?KAIRqz(5lL0Y-TfX9HvK3J5b3C->i5-&&ZsnK&vr znwXk6n%EkFhcGj7F+E)p5I{vTu{HiXy{Gs5Z}a>+KSohI7h7it8!Mx%g|U+sg!O3{ zgyrvOFuA{HZ2!*K*#DlfKP^}V!v60X$G-s_e`f;WWcz!K>)(O<-{Ks zZ$2#ly@!?Q-*Z@*|9-Cn`Cp~~^vM64^nr?i4RiiaM^sFl>|7kd_JJ)IcXyUlbvAG| z0iPvR*&%;t3O;c_{;nOUfu^FNrHPR_`y$06(Z|Pu| zgq`iv7zt*`U!gEcut1pqE*D%=ad*kF~L`lw)pQxheTlWYVhn zg_g+5qzM9=VUQ+$0@3#;N3Cvgh+z)o=y|-iYp!mlt_!~!b(3E9+CN*)WOa|Cc#-8W z21nkcA0POZ=s=n1o-2SZrhd3RzQRugH=#-0|@H#n2g&zAPZ+4;)@ zS+1cX 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