diff --git a/Chapitre 8 - Valeurs propres, vecteurs propres, diagonalisation/8.4 Espaces propres.ipynb b/Chapitre 8 - Valeurs propres, vecteurs propres, diagonalisation/8.4 Espaces propres.ipynb index c336b5c..aeb7795 100644 --- a/Chapitre 8 - Valeurs propres, vecteurs propres, diagonalisation/8.4 Espaces propres.ipynb +++ b/Chapitre 8 - Valeurs propres, vecteurs propres, diagonalisation/8.4 Espaces propres.ipynb @@ -1,136 +1,2777 @@ { "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "### Définition 1\n", - "Soient $\\phi:V\t\\to V$ une transformation linéaire d'un espace vectoriel $V$ et $\\lambda \\in \\mathbb{R}$ une valeur propre de $\\phi.$ Alors l'espace propre de $\\phi$ associé à $\\lambda$ est le sous-ensemble de $V$ défini par $E_{\\lambda}=\\{v\\in V: \\phi(v)=\\lambda v\\}$.\n", + "Soient $V$ un espace vectoriel, $\\phi:V\t\\to V$ une transformation linéaire et $\\lambda \\in \\mathbb{R}$ une valeur propre de $\\phi.$ Alors l'espace propre de $\\phi$ associé à $\\lambda$ est le sous-ensemble de $V$ défini par $E_{\\lambda}=\\{v\\in V: \\phi(v)=\\lambda v\\}$.\n", "\n", - "De manière similaire, si $\\lambda\\in \\mathbb{R}$ est une valeur propre de la matrice $A\\in M_{n \\times n}(\\mathbb{R}),$ alors l'espace propre de $A$ associé à $\\lambda$ est le sous-ensemble de $M_{n \\times 1}(\\mathbb{R})$ défini par $E_{\\lambda}=\\{X\\in M_{n \\times 1}(\\mathbb{R}) : AX=\\lambda X\\}$.\n", + "De manière similaire, si $\\lambda\\in \\mathbb{R}$ est une valeur propre de la matrice $A\\in M_{n \\times n}(\\mathbb{R}),$ alors l'espace propre de $A$ associé à $\\lambda$ est le sous-ensemble de $\\mathbb{R}^n$ défini par $E_{\\lambda}=\\{X\\in \\mathbb{R}^n : AX=\\lambda X\\}$.\n", "\n", "### Proposition 2\n", "Le sous-ensemble $E_\\lambda$ est un sous-espace vectoriel." ] }, { "cell_type": "code", - "execution_count": null, + "execution_count": 3, "metadata": {}, - "outputs": [], + "outputs": [ + { + "data": { + "text/html": [ + " \n", + " " + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], "source": [ "# Importation des différentes librairies\n", "import numpy as np\n", "import plotly\n", "import plotly.graph_objects as go\n", "import sympy as sp\n", "import sys, os \n", "sys.path.append('../Librairie')\n", "import AL_Fct as al\n", "from IPython.utils import io\n", "from IPython.display import display, Latex\n", "from Ch8_lib import *" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Exercice 1\n", - "**Trouvez les valeurs propres des matrices ci-dessous puis pour chacune des valeurs propres, trouvez une base de l'espace propre correspondant.**" + "Trouvez les valeurs propres des matrices ci-dessous puis pour chacune des valeurs propres, trouvez une base de l'espace propre correspondant." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ - "$$ A_1 = \\left(\\begin{matrix}-1 & 3\\\\-1 & 3\\end{matrix}\\right) $$ \n", - "$$ A_2 = \\left(\\begin{matrix}4 & 4\\\\3 & 0\\end{matrix}\\right) $$\n", - "\n", - "$$ A_3 = \\left(\\begin{matrix}-1 & 1 & 0\\\\2 & 0 & 0\\\\1 & 1 & -2\\end{matrix}\\right) $$ \n", - "$$ A_4 = \\left(\\begin{matrix}4 & -1 & 6\\\\2 & 1 & 6\\\\2 & -1 & 8\\end{matrix}\\right) $$ " + "\\begin{align*}\n", + "&A_1 = \\left(\\begin{matrix}-1 & 3\\\\-1 & 3\\end{matrix}\\right) & \n", + "& A_2 = \\left(\\begin{matrix}4 & 4\\\\3 & 0\\end{matrix}\\right) &\n", + "& A_3 = \\left(\\begin{matrix}-1 & 1 & 0\\\\2 & 0 & 0\\\\1 & 1 & -2\\end{matrix}\\right) &\n", + "& A_4 = \\left(\\begin{matrix}4 & -1 & 6\\\\2 & 1 & 6\\\\2 & -1 & 8\\end{matrix}\\right) \n", + "\\end{align*}" ] }, { "cell_type": "code", - "execution_count": null, + "execution_count": 4, "metadata": {}, "outputs": [], "source": [ "A_1 = [[-1, 3], [-1, 3]]\n", "A_2 = [[4, 4], [3, 0]]\n", "\n", "A_3 = [[-1, 1, 0], [2, 0, 0], [1, 1, -2]]\n", "A_4 = [[4, -1, 6], [2, 1, 6], [2, -1, 8]]\n" ] }, { "cell_type": "code", - "execution_count": null, + "execution_count": 5, "metadata": {}, - "outputs": [], + "outputs": [ + { + "data": { + "text/latex": [ + "Trouvez une valeur propre de $A = \\left(\\begin{matrix}-1 & 3\\\\-1 & 3\\end{matrix}\\right)$." + ], + "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + }, + { + "data": { + "application/vnd.jupyter.widget-view+json": { + "model_id": "83bf326c86a34008882c83e4ef585c20", + "version_major": 2, + "version_minor": 0 + }, + "text/plain": [ + "FloatText(value=0.0, description='$\\\\lambda: $')" + ] + }, + "metadata": {}, + "output_type": "display_data" + }, + { + "data": { + "application/vnd.jupyter.widget-view+json": { + "model_id": "5f183f71008b49689db25fc84bc8c15a", + "version_major": 2, + "version_minor": 0 + }, + "text/plain": [ + "interactive(children=(Button(description='Run Interact', style=ButtonStyle()), Output()), _dom_classes=('widge…" + ] + }, + "metadata": {}, + "output_type": "display_data" + }, + { + "data": { + "text/latex": [ + "Si vous n'arrivez pas à trouver les valeurs propres, vous pouvez les afficher en cliquant ici." + ], + "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + }, + { + "data": { + "application/vnd.jupyter.widget-view+json": { + "model_id": "84d3c6da14204c8c91544ae33ded35fc", + "version_major": 2, + "version_minor": 0 + }, + "text/plain": [ + "interactive(children=(Button(description='Run Interact', style=ButtonStyle()), Output()), _dom_classes=('widge…" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], "source": [ "# Executez cette cellule pour faire l'exercice pour la matrice donnée en argument de la fonction interactive_basis\n", "interactive_basis(A_1)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Visualisation des espaces propres\n", - "Les espaces propres des matrices $2\\times2$ et $3\\times3$ peuvent être représenté graphiquement.\n", + "Les espaces propres des matrices $2\\times2$ et $3\\times3$ peuvent être représenté graphiquement, car il s'agit de sous-espaces vectoriels de $\\mathbb{R}^2$ et $\\mathbb{R^3}$ respectivement.\n", "\n", "La fonction `plot_eigspace` permet de visualiser les espaces propres associer à chaque valeurs propres d'une matrice $2\\times2$ ou $3\\times3$. Pour utiliser cette function, il suffit de donner comme argument une matrice. Les valeurs propres et leur espace propre associé sont calculés par la fonction et ensuite affichés.\n", "\n", "Utilisez par exemple les matrices de l'**Exercice 1** afin de visualiser les espaces propres dont vous avez calculé les bases." ] }, { "cell_type": "code", - "execution_count": null, + "execution_count": 6, "metadata": {}, - "outputs": [], + "outputs": [ + { + "data": { + "application/vnd.plotly.v1+json": { + "config": { + "linkText": "Export to plot.ly", + "plotlyServerURL": "https://plot.ly", + "showLink": false + }, + "data": [ + { + "line": { + "colorscale": [ + [ + 0, + "rgb(51, 214, 255)" + ], + [ + 0.1, + "rgb(51, 214, 255)" + ], + [ + 0.2, + "rgb(51, 214, 255)" + ], + [ + 0.3, + "rgb(51, 214, 255)" + ], + [ + 0.4, + "rgb(51, 214, 255)" + ], + [ + 0.5, + "rgb(51, 214, 255)" + ], + [ + 0.6, + "rgb(51, 214, 255)" + ], + [ + 0.7, + "rgb(51, 214, 255)" + ], + [ + 0.8, + "rgb(51, 214, 255)" + ], + [ + 0.9, + "rgb(51, 214, 255)" + ], + [ + 1, + "rgb(51, 214, 255)" + ] + ], + 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