{"id":164529,"date":"2022-06-27T09:20:53","date_gmt":"2022-06-27T08:20:53","guid":{"rendered":"https:\/\/datascientest.com\/?p=162879"},"modified":"2023-11-09T14:03:52","modified_gmt":"2023-11-09T14:03:52","slug":"matrice-definition-implementation","status":"publish","type":"post","link":"https:\/\/datascientest.com\/matrice-definition-implementation","title":{"rendered":"Une matrice : d\u00e9finition, impl\u00e9mentation en python"},"content":{"rendered":"\t\t<div data-elementor-type=\"wp-post\" data-elementor-id=\"164529\" class=\"elementor elementor-164529\" data-elementor-post-type=\"post\">\n\t\t\t\t\t\t\t<div class=\"elementor-element elementor-element-3427d1f e-flex e-con-boxed e-con\" data-id=\"3427d1f\" data-element_type=\"container\" data-settings=\"{&quot;content_width&quot;:&quot;boxed&quot;}\">\n\t\t\t\t\t<div class=\"e-con-inner\">\n\t\t\t\t<div class=\"elementor-element elementor-element-d0920de elementor-widget elementor-widget-heading\" data-id=\"d0920de\" data-element_type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t<style>\/*! elementor - v3.15.0 - 02-08-2023 *\/\n.elementor-heading-title{padding:0;margin:0;line-height:1}.elementor-widget-heading .elementor-heading-title[class*=elementor-size-]>a{color:inherit;font-size:inherit;line-height:inherit}.elementor-widget-heading .elementor-heading-title.elementor-size-small{font-size:15px}.elementor-widget-heading .elementor-heading-title.elementor-size-medium{font-size:19px}.elementor-widget-heading .elementor-heading-title.elementor-size-large{font-size:29px}.elementor-widget-heading .elementor-heading-title.elementor-size-xl{font-size:39px}.elementor-widget-heading .elementor-heading-title.elementor-size-xxl{font-size:59px}<\/style><h2 class=\"elementor-heading-title elementor-size-default\">\"Tu prends la pilule bleue, l'histoire s'arr\u00eate l\u00e0, tu te r\u00e9veilles dans ton lit, et tu crois ce que tu veux. Tu prends la pilule rouge, tu restes au Pays des Merveilles et je te montre jusqu'o\u00f9 va le terrier.\" Conna\u00eetre la v\u00e9rit\u00e9 ou rester dans son confort, d\u00e9couvrir la matrice ou n\u2019en rester qu\u2019un objet. <\/h2>\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t<div class=\"elementor-element elementor-element-9f1ef2b e-flex e-con-boxed e-con\" data-id=\"9f1ef2b\" data-element_type=\"container\" data-settings=\"{&quot;content_width&quot;:&quot;boxed&quot;}\">\n\t\t\t\t\t<div class=\"e-con-inner\">\n\t\t\t\t<div class=\"elementor-element elementor-element-3b73cde elementor-widget elementor-widget-text-editor\" data-id=\"3b73cde\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t<style>\/*! elementor - v3.15.0 - 02-08-2023 *\/\n.elementor-widget-text-editor.elementor-drop-cap-view-stacked .elementor-drop-cap{background-color:#69727d;color:#fff}.elementor-widget-text-editor.elementor-drop-cap-view-framed .elementor-drop-cap{color:#69727d;border:3px solid;background-color:transparent}.elementor-widget-text-editor:not(.elementor-drop-cap-view-default) .elementor-drop-cap{margin-top:8px}.elementor-widget-text-editor:not(.elementor-drop-cap-view-default) .elementor-drop-cap-letter{width:1em;height:1em}.elementor-widget-text-editor .elementor-drop-cap{float:left;text-align:center;line-height:1;font-size:50px}.elementor-widget-text-editor .elementor-drop-cap-letter{display:inline-block}<\/style>\t\t\t\t<p><span style=\"font-weight: 400; color: #000000;\">Ce choix corn\u00e9lien du film <a href=\"https:\/\/fr.wikipedia.org\/wiki\/Matrix_(film)\">Matrix<\/a> aura fait r\u00eaver des g\u00e9n\u00e9rations enti\u00e8res et la matrice est devenue une ic\u00f4ne l\u00e9gendaire de la pop culture, elle est rentr\u00e9e dans le vocabulaire commun. Cependant, avant d\u2019\u00eatre un syst\u00e8me d\u00e9velopp\u00e9 par des machines pour exploiter des individus telles des batteries jetables, les matrices sont des outils math\u00e9matiques puissants \u00e0 l\u2019importance consid\u00e9rable dans de nombreux domaines, de l\u2019alg\u00e8bre lin\u00e9aire aux probabilit\u00e9s en passant par les mod\u00e8les markoviens ou la r\u00e9solution de syst\u00e8mes d\u2019\u00e9quations. Nous allons dans cet article pr\u00e9senter cet outil et en voir les premi\u00e8res propri\u00e9t\u00e9s, ainsi que les mani\u00e8res de les impl\u00e9menter en<span style=\"color: #5e36f3;\"> <a style=\"color: #5e36f3;\" href=\"https:\/\/datascientest.com\/python-tout-savoir\">Python<\/a><\/span>.<\/span><\/p>\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t<div class=\"elementor-element elementor-element-8bbbf5c e-flex e-con-boxed e-con\" data-id=\"8bbbf5c\" data-element_type=\"container\" data-settings=\"{&quot;content_width&quot;:&quot;boxed&quot;}\">\n\t\t\t\t\t<div class=\"e-con-inner\">\n\t\t\t\t<div class=\"elementor-element elementor-element-15c31b6 elementor-widget elementor-widget-heading\" data-id=\"15c31b6\" data-element_type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t<h3 class=\"elementor-heading-title elementor-size-default\">Qu\u2019est-ce qu\u2019une matrice ?<\/h3>\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-4ae4009 elementor-widget elementor-widget-text-editor\" data-id=\"4ae4009\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<p><span style=\"font-weight: 400; color: #000000;\">En math\u00e9matique, une matrice correspond \u00e0 un tableau d&rsquo;\u00e9l\u00e9ments. Il est d\u00e9fini par sa dimension (le nombre de lignes et de colonnes) et par les diff\u00e9rents \u00e9l\u00e9ments pr\u00e9sents dans ce dernier.\u00a0<\/span><\/p>\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-cf3c8fd elementor-widget elementor-widget-image\" data-id=\"cf3c8fd\" data-element_type=\"widget\" data-widget_type=\"image.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t<style>\/*! elementor - v3.15.0 - 02-08-2023 *\/\n.elementor-widget-image{text-align:center}.elementor-widget-image a{display:inline-block}.elementor-widget-image a img[src$=\".svg\"]{width:48px}.elementor-widget-image img{vertical-align:middle;display:inline-block}<\/style>\t\t\t\t\t\t\t\t\t\t\t\t<img decoding=\"async\" src=\"https:\/\/datascientest.com\/wp-content\/uploads\/2022\/06\/matrice-1.png\" title=\"\" alt=\"\" loading=\"lazy\" \/>\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-484b583 elementor-widget elementor-widget-text-editor\" data-id=\"484b583\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<p><span style=\"font-weight: 400; color: #000000;\">Dans cette matrice, n correspond au nombre de colonnes, m correspond au nombre de lignes, i et j sont les indices qui permettent de retrouver un \u00e9l\u00e9ment (\u00e0 la mani\u00e8re des coordonn\u00e9es).<\/span><\/p>\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-1b2a51b elementor-widget elementor-widget-heading\" data-id=\"1b2a51b\" data-element_type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t<h4 class=\"elementor-heading-title elementor-size-default\">Les diff\u00e9rentes matrices usuelles<\/h4>\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-cfd83d5 elementor-widget elementor-widget-text-editor\" data-id=\"cfd83d5\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<ul><li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"color: #000000;\"><span style=\"font-weight: 400;\">Une matrice ne comportant que des \u00e9l\u00e9ments vides est appel\u00e9e la <\/span><b>matrice nulle<\/b>.<\/span><\/li><li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"color: #000000;\"><span style=\"font-weight: 400;\">Lorsqu\u2019il y a le m\u00eame nombre de lignes que de colonnes, on parle de <\/span><b>matrice carr\u00e9e<\/b><\/span><\/li><li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"color: #000000;\"><span style=\"font-weight: 400;\">Une matrice carr\u00e9e n\u2019ayant que des \u00e9l\u00e9ments nuls sauf sur la diagonale est appel\u00e9e <\/span><b>matrice diagonale<\/b><\/span><\/li><li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"color: #000000;\"><span style=\"font-weight: 400;\">Une matrice diagonale ne comportant que des 1 sur la diagonale est appel\u00e9e la <\/span><b>matrice identit\u00e9\u00a0<\/b><\/span><\/li><li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"color: #000000;\"><span style=\"font-weight: 400;\">Une matrice carr\u00e9e ne comportant que des \u00e9l\u00e9ments sous la diagonale est appel\u00e9e <\/span><b>matrice triangulaire inf\u00e9rieure<\/b><\/span><\/li><li style=\"font-weight: 400;\" aria-level=\"1\">Une matrice carr\u00e9e ne comportant que des \u00e9l\u00e9ments au-dessus de la diagonale est appel\u00e9e <span style=\"color: #5e36f3;\"><b><span style=\"color: #000000;\">matrice triangulaire sup\u00e9rieure<\/span><\/b><\/span><\/li><\/ul>\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-63c711c elementor-widget elementor-widget-heading\" data-id=\"63c711c\" data-element_type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t<h4 class=\"elementor-heading-title elementor-size-default\">Les op\u00e9rations sur les matrices<\/h4>\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-d30f8cc elementor-widget elementor-widget-text-editor\" data-id=\"d30f8cc\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<p><span style=\"font-weight: 400;\">Il existe de nombreuses op\u00e9rations que nous pouvons effectuer sur les matrices ou entre elles, nous donnant de nouvelles matrices. Les plus courantes sont les suivantes\u00a0<\/span><b><\/b><\/p><ul><li aria-level=\"1\"><b>La transposition <\/b>: <span style=\"font-weight: 400;\">La transposition correspond \u00e0 la transformation qui transforme les lignes en colonne et inversement, \u00e0 la mani\u00e8re d\u2019un miroir.<\/span><\/li><\/ul>\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-1dab2ec elementor-widget elementor-widget-image\" data-id=\"1dab2ec\" data-element_type=\"widget\" data-widget_type=\"image.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<img decoding=\"async\" width=\"797\" height=\"801\" src=\"https:\/\/datascientest.com\/wp-content\/uploads\/2022\/06\/matric_-la-transposition-1-1.png\" class=\"attachment-full size-full wp-image-163741\" alt=\"\" srcset=\"https:\/\/datascientest.com\/wp-content\/uploads\/2022\/06\/matric_-la-transposition-1-1.png 797w, https:\/\/datascientest.com\/wp-content\/uploads\/2022\/06\/matric_-la-transposition-1-1-150x150.png 150w, https:\/\/datascientest.com\/wp-content\/uploads\/2022\/06\/matric_-la-transposition-1-1-768x772.png 768w\" sizes=\"(max-width: 797px) 100vw, 797px\" \/>\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-9c67f14 elementor-widget elementor-widget-text-editor\" data-id=\"9c67f14\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<ul><li><b>L\u2019addition <\/b>: <span style=\"font-weight: 400;\">l\u2019addition entre matrices de m\u00eame dimension revient \u00e0 additionner chacun des \u00e9l\u00e9ments des matrices.<\/span><\/li><\/ul>\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-cc8ae67 elementor-widget elementor-widget-image\" data-id=\"cc8ae67\" data-element_type=\"widget\" data-widget_type=\"image.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<img decoding=\"async\" src=\"https:\/\/datascientest.com\/wp-content\/uploads\/2022\/06\/Laddition-.png\" title=\"\" alt=\"\" loading=\"lazy\" \/>\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-94dd053 elementor-widget elementor-widget-text-editor\" data-id=\"94dd053\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<ul><li><b>La multiplication par un scalaire <\/b>: <span style=\"font-weight: 400;\">\u00a0Multiplier une matrice par un scalaire correspond \u00e0 la multiplication de chacun des \u00e9l\u00e9ments par ce scalaire (multiplier par k revient \u00e0 additionner k fois les \u00e9l\u00e9ments entre eux).<\/span><\/li><\/ul>\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-9e5f6ef elementor-widget elementor-widget-image\" data-id=\"9e5f6ef\" data-element_type=\"widget\" data-widget_type=\"image.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<img decoding=\"async\" src=\"https:\/\/datascientest.com\/wp-content\/uploads\/2022\/06\/multiplication-par-un-scalaire.png\" title=\"\" alt=\"\" loading=\"lazy\" \/>\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-7f9e06c elementor-widget elementor-widget-text-editor\" data-id=\"7f9e06c\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<ul><li><b>Le produit matriciel<\/b> : <span style=\"font-weight: 400;\">Le produit d\u2019une matrice ligne avec une matrice colonne est d\u00e9fini de la mani\u00e8re suivante :\u00a0<\/span><\/li><\/ul>\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-1b65703 elementor-widget elementor-widget-image\" data-id=\"1b65703\" data-element_type=\"widget\" data-widget_type=\"image.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<img decoding=\"async\" src=\"https:\/\/datascientest.com\/wp-content\/uploads\/2022\/06\/Le-produit-matriciel.png\" title=\"\" alt=\"\" loading=\"lazy\" \/>\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-e9639ac elementor-widget elementor-widget-text-editor\" data-id=\"e9639ac\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<p><span style=\"font-weight: 400; color: #000000;\">\u00c0 partir de cette d\u00e9finition, nous pouvons d\u00e9finir le produit matriciel entre deux matrices. Chaque \u00e9l\u00e9ment d\u2019indice i,j de la matrice produit correspond au produit de la i-\u00e8me ligne et de la j-\u00e8me colonne. Par exemple :\u00a0<\/span><\/p>\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-99f3a24 elementor-widget elementor-widget-image\" data-id=\"99f3a24\" data-element_type=\"widget\" data-widget_type=\"image.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<img decoding=\"async\" src=\"https:\/\/datascientest.com\/wp-content\/uploads\/2022\/06\/matrice-2.png\" title=\"\" alt=\"\" loading=\"lazy\" \/>\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-c5e7094 elementor-widget elementor-widget-text-editor\" data-id=\"c5e7094\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<p><b>Attention : <\/b><span style=\"font-weight: 400;\">Il faut que la premi\u00e8re matrice ait le m\u00eame nombre de lignes que la deuxi\u00e8me en a de colonne et inversement pour que le produit fonctionne bien.<\/span><\/p>\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-ce1cdb3 elementor-widget elementor-widget-heading\" data-id=\"ce1cdb3\" data-element_type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t<h4 class=\"elementor-heading-title elementor-size-default\">Propri\u00e9t\u00e9s du produit matriciel<\/h4>\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-e600289 elementor-widget elementor-widget-text-editor\" data-id=\"e600289\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<ul><li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">Le produit matriciel est :<\/span><ul><li style=\"font-weight: 400;\" aria-level=\"2\"><strong><i>associatif<\/i><\/strong><span style=\"font-weight: 400;\"> : <\/span><b>ABC<\/b><span style=\"font-weight: 400;\"> = (<\/span><b>AB<\/b><span style=\"font-weight: 400;\">)<\/span><b>C<\/b><span style=\"font-weight: 400;\"> = <\/span><b>A<\/b><span style=\"font-weight: 400;\">(<\/span><b>BC<\/b><span style=\"font-weight: 400;\">)<\/span><\/li><li style=\"font-weight: 400;\" aria-level=\"2\"><i><span style=\"font-weight: 400;\"><strong>distributif<\/strong> par rapport \u00e0 l&rsquo;addition<\/span><\/i><span style=\"font-weight: 400;\"> : <\/span><b>A<\/b><span style=\"font-weight: 400;\">(<\/span><b>B<\/b><span style=\"font-weight: 400;\"> + <\/span><b>C<\/b><span style=\"font-weight: 400;\">) = <\/span><b>AB<\/b><span style=\"font-weight: 400;\"> + <\/span><b>AC<\/b><\/li><li style=\"font-weight: 400;\" aria-level=\"2\"><strong><i>non commutatif<\/i><\/strong><span style=\"font-weight: 400;\"> : <\/span><b>AB<\/b><span style=\"font-weight: 400;\"> n&rsquo;est pas \u00e9gal \u00e0 <\/span><b>BA<\/b><span style=\"font-weight: 400;\"> en g\u00e9n\u00e9ral.<\/span><\/li><\/ul><\/li><li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">La matrice unit\u00e9 <\/span><b>I<\/b><span style=\"font-weight: 400;\"> est <\/span><i><span style=\"font-weight: 400;\">\u00e9l\u00e9ment neutre<\/span><\/i><span style=\"font-weight: 400;\"> pour la multiplication : <\/span><b>AI<\/b><span style=\"font-weight: 400;\">m<\/span><span style=\"font-weight: 400;\"> = <\/span><b>I<\/b><span style=\"font-weight: 400;\">n<\/span><b>A<\/b><span style=\"font-weight: 400;\"> = <\/span><b>A<\/b><span style=\"font-weight: 400;\">, si la matrice <\/span><b>A<\/b><span style=\"font-weight: 400;\"> est de dimensions n \u00d7 m.<\/span><\/li><li style=\"font-weight: 400;\" aria-level=\"1\"><span style=\"font-weight: 400;\">Transpos\u00e9e d&rsquo;un produit : (<\/span><b>AB<\/b><span style=\"font-weight: 400;\">)<\/span><span style=\"font-weight: 400;\">T<\/span><span style=\"font-weight: 400;\"> = <\/span><b>B<\/b><span style=\"font-weight: 400;\">T<\/span><b>A<\/b><span style=\"font-weight: 400;\">T<\/span><span style=\"font-weight: 400;\"> (Attention au changement d&rsquo;ordre !).<\/span><\/li><li aria-level=\"1\"><b>Inverse d\u2019une matrice : <\/b><span style=\"font-weight: 400;\">Pour une matrice carr\u00e9e A, s\u2019il existe une matrice B tel que AB vaut l\u2019identit\u00e9, alors BA vaut \u00e9galement l\u2019identit\u00e9, B est unique et s\u2019appelle l\u2019inverse de A. Plus g\u00e9n\u00e9ralement, l\u2019inverse d\u2019une matrice A se note A<\/span><span style=\"font-weight: 400;\">-1<\/span><span style=\"font-weight: 400;\"> .<\/span><\/li><\/ul>\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t<div class=\"elementor-element elementor-element-a84c4ec e-flex e-con-boxed e-con\" data-id=\"a84c4ec\" data-element_type=\"container\" data-settings=\"{&quot;content_width&quot;:&quot;boxed&quot;}\">\n\t\t\t\t\t<div class=\"e-con-inner\">\n\t\t\t\t<div class=\"elementor-element elementor-element-5199f85 elementor-widget elementor-widget-heading\" data-id=\"5199f85\" data-element_type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t<h3 class=\"elementor-heading-title elementor-size-default\">Impl\u00e9mentation en Python<\/h3>\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-37379e4 elementor-widget elementor-widget-text-editor\" data-id=\"37379e4\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<p><span style=\"font-weight: 400; color: #000000;\">Pour impl\u00e9menter des matrices en Python, on peut passer par des listes \u00e0 deux dimensions ou des tableaux<span style=\"color: #5e36f3;\"> <a style=\"color: #5e36f3;\" href=\"https:\/\/datascientest.com\/numpy\">Numpy<\/a><\/span>. Voici un script pr\u00e9sentant des exemples d\u2019utilisation :<\/span><\/p>\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-d09508a elementor-widget elementor-widget-shortcode\" data-id=\"d09508a\" data-element_type=\"widget\" data-widget_type=\"shortcode.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<div class=\"elementor-shortcode\"><script src=\"https:\/\/gist.github.com\/zaxaheb-dst\/fa6660ced76fec1d91816ebfb17dcd7b.js\"><\/script><\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-12aa75f elementor-widget elementor-widget-text-editor\" data-id=\"12aa75f\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<p><span style=\"font-weight: 400; color: #000000;\">Les matrices n\u2019ont dor\u00e9navant aucun secret pour vous, vous avez toutes les cartes en main pour comprendre ces objets qui sont bien plus puissants que Neo ou Morpheus.<\/span><\/p>\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-e961535 elementor-align-center button-principale elementor-widget elementor-widget-button\" data-id=\"e961535\" data-element_type=\"widget\" data-widget_type=\"button.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<div class=\"elementor-button-wrapper\">\n\t\t\t<a class=\"elementor-button elementor-button-link elementor-size-sm elementor-animation-grow\" href=\"https:\/\/datascientest.com\/formations-data\">\n\t\t\t\t\t\t<span class=\"elementor-button-content-wrapper\">\n\t\t\t\t\t\t<span class=\"elementor-button-text\">D\u00e9couvrir les formations<\/span>\n\t\t<\/span>\n\t\t\t\t\t<\/a>\n\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t\t\t<\/div>\n\t\t","protected":false},"excerpt":{"rendered":"<p>\u00ab\u00a0Tu prends la pilule bleue, l&rsquo;histoire s&rsquo;arr\u00eate l\u00e0, tu te r\u00e9veilles dans ton lit, et tu crois ce que tu veux. Tu prends la pilule rouge, tu restes au Pays des Merveilles et je te montre jusqu&rsquo;o\u00f9 va le terrier.\u00a0\u00bb Conna\u00eetre la v\u00e9rit\u00e9 ou rester dans son confort, d\u00e9couvrir la matrice ou n\u2019en rester qu\u2019un [&hellip;]<\/p>\n","protected":false},"author":77,"featured_media":165043,"comment_status":"open","ping_status":"open","sticky":false,"template":"elementor_theme","format":"standard","meta":{"content-type":"","inline_featured_image":false},"categories":[2497],"tags":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO Premium plugin v21.7 (Yoast SEO v21.7) - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>Une matrice : d\u00e9finition, impl\u00e9mentation en python<\/title>\n<meta name=\"description\" content=\"Une matrice correspond \u00e0 un tableau d&#039;\u00e9l\u00e9ments. 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