{"id":471,"date":"2026-10-03T06:00:15","date_gmt":"2026-10-03T03:00:15","guid":{"rendered":"https:\/\/wpcalc.com\/fr\/?p=471"},"modified":"2026-10-03T06:00:15","modified_gmt":"2026-10-03T03:00:15","slug":"multiplication-matrices","status":"publish","type":"post","link":"https:\/\/wpcalc.com\/fr\/mathematiques\/multiplication-matrices\/","title":{"rendered":"Calculateur de multiplication de matrices"},"content":{"rendered":"<style id=\"wpcoderpro-inline-472\">.calculator input[readonly] {\r\n\toutline-color: oklch(70.4% 0.191 22.216);\r\n}<\/style><section class=\"not-prose calculator-box\" aria-labelledby=\"calculator-title\"><div class=\"flex items-baseline sm:items-center justify-between gap-2 sm:gap-3\"><div class=\"flex flex-col sm:flex-row sm:items-center gap-2\"><span class=\"icon icon-calculator text-primary-700! text-base! dark:text-primary-300!\" aria-hidden=\"true\"><\/span><h2 id=\"calculator-title\" class=\"text-lg font-display font-bold\">Outil de multiplication de matrices<\/h2><\/div><div class=\"calcdash-favorite group\">\n  <button type=\"button\" class=\"favorite\" id=\"favorite\" data-favorite-id=\"471\" data-favorite-title=\"Multiplication de matrices\" data-favorite-url=\"https:\/\/wpcalc.com\/fr\/mathematiques\/multiplication-matrices\/\" data-favorite-excerpt=\"Multipliez instantan\u00e9ment deux matrices de dimensions compatibles (jusqu\u2019\u00e0 3 \u00d7 3). Choisissez les dimensions des matrices A et B, saisissez leurs \u00e9l\u00e9ments et obtenez la matrice produit compl\u00e8te A \u00d7 B.\" aria-label=\"Ajouter aux favoris\" data-favorite-icon=\"icon icon-binary\">\n    <span class=\"icon icon-shape-star-empty\" aria-hidden=\"true\"><\/span>\n  <\/button>\n  <div class=\"calcdash-favorite__tip\" aria-hidden=\"true\">\n   <span class=\"favorite-tooltip\" id=\"favorite-tooltip\"><\/span>\n  <\/div>\n  <span class=\"sr-only\" role=\"status\" id=\"favorite-status\"><\/span>\n<\/div><\/div><form action=\"https:\/\/wpcalc.com\/fr\/mathematiques\/multiplication-matrices\/\" method=\"POST\" class=\"calculator\" id=\"calculator-471\" data-post=\"471\"><fieldset class=\"fieldset-input is-3\"><legend class=\"sr-only\">Champs de saisie<\/legend><div class=\"field is-single\" id=\"input-1\"><label for=\"field-1\">Dimensions de la matrice A<\/label><div class=\"grid grid-cols-1\"><select id=\"field-1\" name=\"dimensions_de_la_matrice_a\"><option value=\"3x3\">3 \u00d7 3<\/option><option value=\"3x2\">3 \u00d7 2<\/option><option value=\"2x3\">2 \u00d7 3<\/option><option value=\"3x1\">3 \u00d7 1<\/option><option value=\"1x3\">1 \u00d7 3<\/option><option value=\"2x2\">2 \u00d7 2<\/option><\/select><svg class=\"pointer-events-none col-start-1 row-start-1 mr-2 size-5 self-center justify-self-end text-gray-500 sm:size-4\" viewBox=\"0 0 16 16\" fill=\"currentColor\" aria-hidden=\"true\" data-slot=\"icon\">\n              <path fill-rule=\"evenodd\" d=\"M4.22 6.22a.75.75 0 0 1 1.06 0L8 8.94l2.72-2.72a.75.75 0 1 1 1.06 1.06l-3.25 3.25a.75.75 0 0 1-1.06 0L4.22 7.28a.75.75 0 0 1 0-1.06Z\" clip-rule=\"evenodd\" \/>\n            <\/svg><\/div><\/div><div class=\"field is-single\" id=\"input-2\"><label for=\"field-2\">Dimensions de la matrice B<\/label><div class=\"grid grid-cols-1\"><select id=\"field-2\" name=\"dimensions_de_la_matrice_b\"><option value=\"3x3\">3 \u00d7 3<\/option><option value=\"3x2\">3 \u00d7 2<\/option><option value=\"2x3\">2 \u00d7 3<\/option><option value=\"3x1\">3 \u00d7 1<\/option><option value=\"1x3\">1 \u00d7 3<\/option><option value=\"2x2\">2 \u00d7 2<\/option><\/select><svg class=\"pointer-events-none col-start-1 row-start-1 mr-2 size-5 self-center justify-self-end text-gray-500 sm:size-4\" viewBox=\"0 0 16 16\" fill=\"currentColor\" aria-hidden=\"true\" data-slot=\"icon\">\n              <path fill-rule=\"evenodd\" d=\"M4.22 6.22a.75.75 0 0 1 1.06 0L8 8.94l2.72-2.72a.75.75 0 1 1 1.06 1.06l-3.25 3.25a.75.75 0 0 1-1.06 0L4.22 7.28a.75.75 0 0 1 0-1.06Z\" clip-rule=\"evenodd\" \/>\n            <\/svg><\/div><\/div><div class=\"is-single field\" id=\"input-3\"><span class=\"font-semibold\">Matrice A<\/span><\/div><div class=\"field\" id=\"input-4\"><label for=\"field-4\">A11<\/label><input type=\"number\" name=\"a11\" id=\"field-4\" step=\"any\" value=\"1\"\/><\/div><div class=\"field\" id=\"input-5\"><label for=\"field-5\">A12<\/label><input type=\"number\" name=\"a12\" id=\"field-5\" step=\"any\" value=\"2\"\/><\/div><div class=\"field\" id=\"input-6\"><label for=\"field-6\">A13<\/label><input type=\"number\" name=\"a13\" id=\"field-6\" step=\"any\" value=\"3\"\/><\/div><div class=\"field\" id=\"input-7\"><label for=\"field-7\">A21<\/label><input type=\"number\" name=\"a21\" id=\"field-7\" step=\"any\" value=\"4\"\/><\/div><div class=\"field\" id=\"input-8\"><label for=\"field-8\">A22<\/label><input type=\"number\" name=\"a22\" id=\"field-8\" step=\"any\" value=\"5\"\/><\/div><div class=\"field\" id=\"input-9\"><label for=\"field-9\">A23<\/label><input type=\"number\" name=\"a23\" id=\"field-9\" step=\"any\" value=\"6\"\/><\/div><div class=\"field\" id=\"input-10\"><label for=\"field-10\">A31<\/label><input type=\"number\" name=\"a31\" id=\"field-10\" step=\"any\" value=\"7\"\/><\/div><div class=\"field\" id=\"input-11\"><label for=\"field-11\">A32<\/label><input type=\"number\" name=\"a32\" id=\"field-11\" step=\"any\" value=\"8\"\/><\/div><div class=\"field\" id=\"input-12\"><label for=\"field-12\">A33<\/label><input type=\"number\" name=\"a33\" id=\"field-12\" step=\"any\" value=\"9\"\/><\/div><div class=\"is-single field\" id=\"input-13\"><span class=\"font-semibold\">Matrice B<\/span><\/div><div class=\"field\" id=\"input-14\"><label for=\"field-14\">B11<\/label><input type=\"number\" name=\"b11\" id=\"field-14\" step=\"any\" value=\"9\"\/><\/div><div class=\"field\" id=\"input-15\"><label for=\"field-15\">B12<\/label><input type=\"number\" name=\"b12\" id=\"field-15\" step=\"any\" value=\"8\"\/><\/div><div class=\"field\" id=\"input-16\"><label for=\"field-16\">B13<\/label><input type=\"number\" name=\"b13\" id=\"field-16\" step=\"any\" value=\"7\"\/><\/div><div class=\"field\" id=\"input-17\"><label for=\"field-17\">B21<\/label><input type=\"number\" name=\"b21\" id=\"field-17\" step=\"any\" value=\"6\"\/><\/div><div class=\"field\" id=\"input-18\"><label for=\"field-18\">B22<\/label><input type=\"number\" name=\"b22\" id=\"field-18\" step=\"any\" value=\"5\"\/><\/div><div class=\"field\" id=\"input-19\"><label for=\"field-19\">B23<\/label><input type=\"number\" name=\"b23\" id=\"field-19\" step=\"any\" value=\"4\"\/><\/div><div class=\"field\" id=\"input-20\"><label for=\"field-20\">B31<\/label><input type=\"number\" name=\"b31\" id=\"field-20\" step=\"any\" value=\"3\"\/><\/div><div class=\"field\" id=\"input-21\"><label for=\"field-21\">B32<\/label><input type=\"number\" name=\"b32\" id=\"field-21\" step=\"any\" value=\"2\"\/><\/div><div class=\"field\" id=\"input-22\"><label for=\"field-22\">B33<\/label><input type=\"number\" name=\"b33\" id=\"field-22\" step=\"any\" value=\"1\"\/><\/div><\/fieldset><div class=\"buttons\"><button type=\"submit\" data-text=\"Recalculer\" id=\"calculate-button\" data-post=\"471\">Calculer<\/button><button type=\"reset\">R\u00e9initialiser<\/button><\/div><div class=\"field is-checkbox hidden!\" id=\"field-auto-calc\"><input type=\"checkbox\" id=\"auto-calc\"><label for=\"auto-calc\">Calculer automatiquement<\/label><small>Si activ\u00e9, le r\u00e9sultat se met \u00e0 jour automatiquement d\u00e8s que vous modifiez une valeur.<\/small><\/div><div class=\"fieldset-result is-hidden\" aria-labelledby=\"result-title\" aria-live=\"polite\" role=\"region\"> <h3 class=\"result-title bg-gradient-to-r from-primary-50 to-gray-50 dark:from-primary-900 dark:to-gray-800\" id=\"result-title\"><span class=\"icon icon-s-pulse\" aria-hidden=\"true\"><\/span> Vos r\u00e9sultats<\/h3><div class=\"result-box\"><div class=\"field-result is-column\" id=\"output-1\"><span class=\"field-title\"><span>R\u00e9sultat de la multiplication des matrices (A \u00d7 B)<\/span><\/span><span class=\"field-value\" id=\"result-1\"><\/span><button type=\"button\" class=\"copy-result\" data-tooltip=\"Copier le r\u00e9sultat\" aria-label=\"Copier le r\u00e9sultat\"><span class=\"copy-icon icon icon-document-copy\" aria-hidden=\"true\"><\/span><\/button><\/div><\/div><div class=\"result-actions\"><button type=\"button\" class=\"copy-link\"><svg viewBox=\"0 0 20 20\" fill=\"currentColor\" aria-hidden=\"true\"><path d=\"M12.232 4.232a2.5 2.5 0 0 1 3.536 3.536l-1.225 1.224a.75.75 0 0 0 1.061 1.06l1.224-1.224a4 4 0 0 0-5.656-5.656l-3 3a4 4 0 0 0 .225 5.865.75.75 0 0 0 .977-1.138 2.5 2.5 0 0 1-.142-3.667l3-3Z\"\/><path d=\"M11.603 7.963a.75.75 0 0 0-.977 1.138 2.5 2.5 0 0 1 .142 3.667l-3 3a2.5 2.5 0 0 1-3.536-3.536l1.225-1.224a.75.75 0 0 0-1.061-1.06l-1.224 1.224a4 4 0 1 0 5.656 5.656l3-3a4 4 0 0 0-.225-5.865Z\"\/><\/svg><span class=\"copy-link__text\">Copier le lien vers ce calcul<\/span><\/button><span class=\"sr-only\" role=\"status\" id=\"copy-link-status\"><\/span><\/div><\/div><a href=\"#respond\" class=\"hidden transition-opacity duration-300 opacity-0 w-50 text-sm justify-center items-center gap-2 px-4 py-2 rounded bg-gray-200 text-gray-700 hover:bg-gray-300\" id=\"leave-comment\"><span class=\"icon icon-comments\" aria-hidden=\"true\"><\/span>Laisser un commentaire<\/a><\/form><\/section><section id=\"calc-reactions\" class=\"not-prose hidden my-12 bg-gradient-to-r from-primary-50 to-gray-50 border border-indigo-100 rounded-xl px-6 py-4 shadow-sm\" data-post=\"471\" aria-live=\"polite\" aria-labelledby=\"calc-reactions-title\"><p id=\"calc-reactions-title\" class=\"text-sm text-gray-500 text-center mb-2\">Que pensez-vous de ce r\u00e9sultat\u00a0?<\/p><div role=\"group\" aria-labelledby=\"calc-reactions-title\" class=\"grid grid-cols-3 sm:flex sm:flex-row sm:justify-around gap-4 sm:items-center sm:flex-wrap\"><button type=\"button\" aria-pressed=\"false\" class=\"reaction-btn flex flex-col items-center gap-1 text-sm text-gray-700 hover:text-primary-600 cursor-pointer transition-transform hover:scale-105\" data-reaction=\"like\"><span class=\"reaction-count\" data-reaction-count=\"like\">0<\/span><span class=\"reaction text-3xl\" aria-hidden=\"true\">\ud83d\ude00 <\/span><span class=\"reaction-description font-medium\">J\u2019aime <\/span><\/button><button type=\"button\" aria-pressed=\"false\" class=\"reaction-btn flex flex-col items-center gap-1 text-sm text-gray-700 hover:text-primary-600 cursor-pointer transition-transform hover:scale-105\" data-reaction=\"helpful\"><span class=\"reaction-count\" data-reaction-count=\"helpful\">0<\/span><span class=\"reaction text-3xl\" aria-hidden=\"true\">\ud83d\udca1 <\/span><span class=\"reaction-description font-medium\">Utile <\/span><\/button><button type=\"button\" aria-pressed=\"false\" class=\"reaction-btn flex flex-col items-center gap-1 text-sm text-gray-700 hover:text-primary-600 cursor-pointer transition-transform hover:scale-105\" data-reaction=\"confused\"><span class=\"reaction-count\" data-reaction-count=\"confused\">0<\/span><span class=\"reaction text-3xl\" aria-hidden=\"true\">\ud83d\ude15 <\/span><span class=\"reaction-description font-medium\">Confus <\/span><\/button><button type=\"button\" aria-pressed=\"false\" class=\"reaction-btn flex flex-col items-center gap-1 text-sm text-gray-700 hover:text-primary-600 cursor-pointer transition-transform hover:scale-105\" data-reaction=\"disappointed\"><span class=\"reaction-count\" data-reaction-count=\"disappointed\">0<\/span><span class=\"reaction text-3xl\" aria-hidden=\"true\">\ud83d\ude1e <\/span><span class=\"reaction-description font-medium\">D\u00e9\u00e7u <\/span><\/button><button type=\"button\" aria-pressed=\"false\" class=\"reaction-btn flex flex-col items-center gap-1 text-sm text-gray-700 hover:text-primary-600 cursor-pointer transition-transform hover:scale-105\" data-reaction=\"inaccurate\"><span class=\"reaction-count\" data-reaction-count=\"inaccurate\">0<\/span><span class=\"reaction text-3xl\" aria-hidden=\"true\">\u274c <\/span><span class=\"reaction-description font-medium\">Inexact <\/span><\/button><\/div><div id=\"reaction-message\" class=\"hidden mt-8 rounded-md border border-primary-100 bg-white\/50 backdrop-blur-sm px-4 py-2 text-sm text-center shadow-sm\"><\/div><\/section><div class=\"calcdash-ad not-prose calcdash-ad--calc_result calcdash-ad--in-article\"><ins class=\"adsbygoogle\" style=\"display:block\" data-ad-client=\"ca-pub-1721569815777345\" data-ad-slot=\"6317458308\" data-ad-layout=\"in-article\" data-ad-format=\"fluid\"><\/ins><script>(adsbygoogle = window.adsbygoogle || []).push({});<\/script><\/div>\n<style id=\"wpcoderpro-inline-1\">.formula-box {\r\n\tborder-bottom: none !important;\r\n}<\/style><section class=\"formula-box\" aria-labelledby=\"formula-title\">\r\n\t<div id=\"formula-title\" class=\"not-prose font-display mb-4\"><span class=\"icon icon-formula\" aria-hidden=\"true\"><\/span><h2>Formule de multiplication de matrices<\/h2><\/div>\r\n\t<figure class=\"not-prose formula\">\r\n\t\t<figcaption class=\"formula-title\">Formule<\/figcaption>\r\n\t\t<div class=\"text-base text-gray-800\" id=\"formula\">\n\\[ C_{ij} = \\sum_{k=1}^{n} A_{ik} B_{kj} \\]\n<\/div>\r\n\t<\/figure>\r\n\t<\/p>\n<p><strong>O\u00f9&nbsp;:<\/strong><\/p>\n<ul>\n<li>\\(C_{ij}\\) \u2014 \u00e9l\u00e9ment situ\u00e9 \u00e0 la ligne \\(i\\), colonne \\(j\\) de la matrice produit<\/li>\n<li>\\(A_{ik}\\) \u2014 \u00e9l\u00e9ment situ\u00e9 \u00e0 la ligne \\(i\\), colonne \\(k\\) de la matrice A<\/li>\n<li>\\(B_{kj}\\) \u2014 \u00e9l\u00e9ment situ\u00e9 \u00e0 la ligne \\(k\\), colonne \\(j\\) de la matrice B<\/li>\n<li>\\(n\\) \u2014 dimension commune&nbsp;: le nombre de colonnes de A, qui doit \u00eatre \u00e9gal au nombre de lignes de B<\/li>\n<\/ul>\n<p>Chaque \u00e9l\u00e9ment du produit est la somme des produits des \u00e9l\u00e9ments correspondants d\u2019une ligne de A et d\u2019une colonne de B&nbsp;: c\u2019est la r\u00e8gle classique \u00ab&nbsp;ligne par colonne&nbsp;\u00bb.<\/p>\n<p>\r\n<\/section>\n<style id=\"wpcoderpro-inline-2\">.calculation-box {\r\n\tborder-bottom: none !important;\r\n}<\/style><section id=\"calculation\" class=\"calculation-box\" aria-labelledby=\"calculation-title\">\r\n\t<div id=\"calculation-title\" class=\"not-prose font-display\"><span class=\"icon icon-unordered-list\" aria-hidden=\"true\"><\/span><h2>Multiplication de matrices \u2013 exemple de calcul<\/h2><\/div>\r\n\r\n<\/p>\n<p><strong>Exemple&nbsp;:<\/strong> multiplions deux matrices 3 \u00d7 3 (il s\u2019agit des valeurs par d\u00e9faut du calculateur, ce qui vous permet de reproduire le r\u00e9sultat ci-dessus).<\/p>\n<p>\\[ A = \\begin{bmatrix} 1 &amp; 2 &amp; 3 \\\\ 4 &amp; 5 &amp; 6 \\\\ 7 &amp; 8 &amp; 9 \\end{bmatrix}, \\quad B = \\begin{bmatrix} 9 &amp; 8 &amp; 7 \\\\ 6 &amp; 5 &amp; 4 \\\\ 3 &amp; 2 &amp; 1 \\end{bmatrix} \\]<\/p>\n<p>Prenons la ligne 1 de A et la colonne 1 de B : \\( 1 \\cdot 9 + 2 \\cdot 6 + 3 \\cdot 3 = 30 \\). En r\u00e9p\u00e9tant l\u2019op\u00e9ration pour chaque paire ligne-colonne, on obtient :<\/p>\n<p>\\[ C = A \\times B = \\begin{bmatrix} 30 &amp; 24 &amp; 18 \\\\ 84 &amp; 69 &amp; 54 \\\\ 138 &amp; 114 &amp; 90 \\end{bmatrix} \\]<\/p>\n<p><strong>R\u00e9sultat&nbsp;:<\/strong> une matrice 3 \u00d7 3 dont le premier \u00e9l\u00e9ment est 30, le deuxi\u00e8me 24, et ainsi de suite.<\/p>\n<p>\n\r\n<\/section>\n<h2>Comment utiliser le calculateur<\/h2>\n<ol>\n<li>D\u00e9finissez les <strong>dimensions de la matrice A<\/strong> (par exemple 3 \u00d7 3) et les <strong>dimensions de la matrice B<\/strong> \u00e0 l\u2019aide des menus d\u00e9roulants. Le nombre de colonnes de A doit \u00eatre \u00e9gal au nombre de lignes de B&nbsp;; sinon, le calculateur signale que les dimensions sont incompatibles.<\/li>\n<li>Saisissez les \u00e9l\u00e9ments de la <strong>matrice A<\/strong> dans les champs A11, A12, \u2026 Les champs situ\u00e9s en dehors des dimensions choisies deviennent non modifiables et sont ignor\u00e9s.<\/li>\n<li>Saisissez les \u00e9l\u00e9ments de la <strong>matrice B<\/strong> dans les champs B11, B12, \u2026<\/li>\n<li>Consultez la matrice produit <strong>A \u00d7 B<\/strong> dans le tableau des r\u00e9sultats. Ses dimensions sont (nombre de lignes de A) \u00d7 (nombre de colonnes de B).<\/li>\n<\/ol>\n<h2>Qu\u2019est-ce que la multiplication de matrices ?<\/h2>\n<p>La multiplication de matrices est une op\u00e9ration binaire qui combine deux matrices pour en former une nouvelle. Contrairement \u00e0 la multiplication ordinaire des nombres, elle ne s\u2019effectue <em>pas<\/em> \u00e9l\u00e9ment par \u00e9l\u00e9ment : chaque \u00e9l\u00e9ment du r\u00e9sultat est le produit scalaire d\u2019une ligne de la premi\u00e8re matrice et d\u2019une colonne de la seconde. Une matrice A de dimensions \\(m \\times n\\) peut \u00eatre multipli\u00e9e par une matrice B de dimensions \\(n \\times p\\), et le r\u00e9sultat est de dimensions \\(m \\times p\\).<\/p>\n<p>L\u2019ordre de multiplication est important. En g\u00e9n\u00e9ral, \\(AB \\neq BA\\), et il arrive m\u00eame qu\u2019un seul des deux produits soit d\u00e9fini. Lorsque vous calculez \\(A \\times B\\), vous multipliez les <em>lignes de A par les colonnes de B<\/em> : inverser les matrices donne une op\u00e9ration diff\u00e9rente (ou impossible).<\/p>\n<p>Les produits matriciels sont omnipr\u00e9sents en math\u00e9matiques appliqu\u00e9es : ils servent \u00e0 transformer des points et des objets en infographie, \u00e0 encha\u00eener des transformations en robotique, \u00e0 r\u00e9soudre des syst\u00e8mes d\u2019\u00e9quations lin\u00e9aires et \u00e0 faire fonctionner les couches des r\u00e9seaux de neurones en apprentissage automatique. Multiplier une matrice par elle-m\u00eame donne son carr\u00e9, que vous pouvez calculer avec le <a href=\"https:\/\/wpcalc.com\/fr\/mathematiques\/matrice-au-carre\/\">calculateur de carr\u00e9 d\u2019une matrice<\/a>.<\/p>\n<h2>Interpr\u00e9ter le r\u00e9sultat<\/h2>\n<p>Le tableau des r\u00e9sultats affiche la matrice produit \\(C\\), qui comporte \\(m\\) lignes et \\(p\\) colonnes. Chaque \u00e9l\u00e9ment \\(C_{ij}\\) est obtenu en multipliant terme \u00e0 terme la \\(i\\)-\u00e8me ligne de A par la \\(j\\)-\u00e8me colonne de B, puis en additionnant les produits. Si les \u00e9l\u00e9ments d\u2019une ligne de A sont multipli\u00e9s dans le mauvais ordre, le r\u00e9sultat sera erron\u00e9 : c\u2019est pr\u00e9cis\u00e9ment le type d\u2019erreur que ce calculateur \u00e9vite.<\/p>\n<p>Si vous devez aussi combiner des matrices \u00e9l\u00e9ment par \u00e9l\u00e9ment, utilisez plut\u00f4t les calculateurs d\u2019<a href=\"https:\/\/wpcalc.com\/fr\/mathematiques\/addition-de-deux-matrices\/\">addition de matrices<\/a> ou de <a href=\"https:\/\/wpcalc.com\/fr\/mathematiques\/soustraction-matrices\/\">soustraction de matrices<\/a> : ces op\u00e9rations s\u2019effectuent \u00e9l\u00e9ment par \u00e9l\u00e9ment et n\u00e9cessitent des dimensions identiques.<\/p>\n<h2>Conditions, limites et conseils<\/h2>\n<ul>\n<li><strong>Dimensions maximales&nbsp;:<\/strong> ce calculateur accepte les matrices jusqu\u2019\u00e0 3 \u00d7 3. Les produits de matrices plus grandes se calculent de la m\u00eame mani\u00e8re, mais n\u00e9cessitent un logiciel ou un calcul \u00e0 la main.<\/li>\n<li><strong>R\u00e8gle de compatibilit\u00e9&nbsp;:<\/strong> la multiplication n\u2019est d\u00e9finie que si le nombre de colonnes de A est \u00e9gal au nombre de lignes de B. Le produit d\u2019une matrice 2 \u00d7 3 par une matrice 3 \u00d7 2 est possible (r\u00e9sultat 2 \u00d7 2) ; le produit d\u2019une matrice 3 \u00d7 2 par une matrice 2 \u00d7 3 l\u2019est aussi (r\u00e9sultat 3 \u00d7 3), mais les r\u00e9sultats sont diff\u00e9rents.<\/li>\n<li><strong>Non-commutativit\u00e9&nbsp;:<\/strong> puisque \\(AB \\neq BA\\) en g\u00e9n\u00e9ral, v\u00e9rifiez toujours quelle matrice vient en premier dans votre probl\u00e8me.<\/li>\n<li><strong>Propri\u00e9t\u00e9 des d\u00e9terminants&nbsp;:<\/strong> pour des matrices carr\u00e9es, \\(\\det(AB) = \\det(A) \\cdot \\det(B)\\). Vous pouvez le v\u00e9rifier avec le <a href=\"https:\/\/wpcalc.com\/fr\/mathematiques\/produit-determinants\/\">calculateur du d\u00e9terminant d\u2019un produit de matrices<\/a>.<\/li>\n<li><strong>Applications&nbsp;:<\/strong> si le produit intervient dans d\u2019autres calculs d\u2019alg\u00e8bre lin\u00e9aire, par exemple pour trouver une matrice inverse, le <a href=\"https:\/\/wpcalc.com\/fr\/mathematiques\/calculateur-inverse-matrice-3x3\/\">calculateur d\u2019inverse d\u2019une matrice 3 \u00d7 3<\/a> permet de passer \u00e0 l\u2019\u00e9tape suivante.<\/li>\n<\/ul>\n","protected":false},"excerpt":{"rendered":"<p>Multipliez instantan\u00e9ment deux matrices de dimensions compatibles (jusqu\u2019\u00e0 3 \u00d7 3). Choisissez les dimensions des matrices A et B, saisissez leurs \u00e9l\u00e9ments et obtenez la matrice produit compl\u00e8te A \u00d7 B.<\/p>\n","protected":false},"author":3168,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"footnotes":""},"categories":[2],"tags":[24],"class_list":["post-471","post","type-post","status-publish","format-standard","hentry","category-mathematiques","tag-matrices"],"acf":[],"_links":{"self":[{"href":"https:\/\/wpcalc.com\/fr\/wp-json\/wp\/v2\/posts\/471","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/wpcalc.com\/fr\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/wpcalc.com\/fr\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/wpcalc.com\/fr\/wp-json\/wp\/v2\/users\/3168"}],"replies":[{"embeddable":true,"href":"https:\/\/wpcalc.com\/fr\/wp-json\/wp\/v2\/comments?post=471"}],"version-history":[{"count":8,"href":"https:\/\/wpcalc.com\/fr\/wp-json\/wp\/v2\/posts\/471\/revisions"}],"predecessor-version":[{"id":5109,"href":"https:\/\/wpcalc.com\/fr\/wp-json\/wp\/v2\/posts\/471\/revisions\/5109"}],"wp:attachment":[{"href":"https:\/\/wpcalc.com\/fr\/wp-json\/wp\/v2\/media?parent=471"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/wpcalc.com\/fr\/wp-json\/wp\/v2\/categories?post=471"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/wpcalc.com\/fr\/wp-json\/wp\/v2\/tags?post=471"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}