diff --git "a/Chapitre 3 - Espace vectoriel/3.1. D\303\251finition d'un espace vectoriel.ipynb" "b/Chapitre 3 - Espace vectoriel/3.1. D\303\251finition d'un espace vectoriel.ipynb" index d2ae04f..d42c205 100644 --- "a/Chapitre 3 - Espace vectoriel/3.1. D\303\251finition d'un espace vectoriel.ipynb" +++ "b/Chapitre 3 - Espace vectoriel/3.1. D\303\251finition d'un espace vectoriel.ipynb" @@ -1,30 +1,1020 @@ { "cells": [ { "cell_type": "markdown", "metadata": {}, + "source": [ + "# Concept(s)-clé(s) et théorie\n", + "\n", + "Soit $V$ un ensemble non-vide muni d'une opération binaire $+$ et d'une action sur les nombres réels $\\cdot$, c'est-à-dire que pour tout $u,v\\in V$, il existe un unique élément $u+v\\in V$ et pour tout $u\\in V$, $\\lambda\\in \\mathbb{R}$, il existe un unique élément $\\lambda\\cdot u\\in V$. On dira que $V$ est un $\\mathbb{R}$-espace vectoriel si les huit axiomes suivants sont satisfaits, pour tous $u,v,w\\in V$ et $\\lambda, \\mu\\in \\mathbb{R}$.\n", + "\n", + "\n", + "1. $u+ v=v+ u$\n", + "2. $(u+ v) + w = u + (v+ w)$\n", + "3. $\\lambda\\cdot( u + v)= \\lambda \\cdot u + \\lambda \\cdot v$\n", + "4. $(\\lambda + \\mu)\\cdot v=\\lambda \\dot v + \\mu\\cdot v$\n", + "5. $\\lambda \\cdot (\\mu\\cdot v)=(\\lambda \\mu)\\cdot v$\n", + "6. $1\\cdot u=u$\n", + "7. Il existe un élément neutre pour la loi $+$, i.e. un élément $e\\in V$ tel que $e+ u=u$ pour tout $u\\in V$.\n", + "8. Pour tout $u\\in V$, il existe un unique inverse par rapport à la loi $+$, i.e. un élément $u' \\in V$ tel que $u+ u'=e$. \n", + "\n", + "Remarques: \n", + "1. On écrit $\\lambda v$ au lieu de $\\lambda \\cdot v$. \n", + "2. Les éléments de $V$ sont appelés des vecteurs (même si on ne les écrit pas $\\overrightarrow v$) et les éléments de $\\mathbb{R}$ des scalaires.\n", + "\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "L'espace vectoriel des polynômes est " + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Pour rentrer un polyôme ou une fonction, utilisez la syntaxe suivante\n", + "\n", + "$\n", + "p(t)=a_\n", + "$" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": {}, + "outputs": [ + { + "data": { + "application/vnd.plotly.v1+json": { + "config": { + "plotlyServerURL": "https://plot.ly" + }, + "data": [ + { + "type": "scatter", + "x": [ + -10, + -9, + -8, + -7, + -6, + -5, + -4, + -3, + -2, + -1, + 0, + 1, + 2, + 3, + 4, + 5, + 6, + 7, + 8, + 9 + ], + "y": [ + -1000, + -729, + -512, + -343, + -216, + -125, + -64, + -27, + -8, + -1, + 0, + 1, + 8, + 27, + 64, + 125, + 216, + 343, + 512, + 729 + ] + } + ], + "layout": { + 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", 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