{"id":303,"date":"2023-07-06T12:10:47","date_gmt":"2023-07-06T12:10:47","guid":{"rendered":"https:\/\/mathority.org\/cn\/%e6%a0%87%e9%87%8f%e7%9f%a9%e9%98%b5\/"},"modified":"2023-07-06T12:10:47","modified_gmt":"2023-07-06T12:10:47","slug":"%e6%a0%87%e9%87%8f%e7%9f%a9%e9%98%b5","status":"publish","type":"post","link":"https:\/\/mathority.org\/cn\/%e6%a0%87%e9%87%8f%e7%9f%a9%e9%98%b5\/","title":{"rendered":"\u6807\u91cf\u77e9\u9635"},"content":{"rendered":"<p>\u5728\u6b64\u9875\u9762\u4e0a\uff0c\u60a8\u5c06\u627e\u5230\u4ec0\u4e48\u662f\u6807\u91cf\u77e9\u9635\u4ee5\u53ca\u6807\u91cf\u77e9\u9635\u7684\u51e0\u4e2a\u793a\u4f8b\uff0c\u4ee5\u4fbf\u5b8c\u5168\u7406\u89e3\u5b83\u3002\u6b64\u5916\uff0c\u60a8\u5c06\u80fd\u591f\u770b\u5230\u6807\u91cf\u77e9\u9635\u7684\u6240\u6709\u5c5e\u6027\u4ee5\u53ca\u4f7f\u7528\u5b83\u4eec\u8fdb\u884c\u8fd0\u7b97\u7684\u4f18\u70b9\u3002\u6700\u540e\uff0c\u6211\u4eec\u89e3\u91ca\u5982\u4f55\u8ba1\u7b97\u6807\u91cf\u77e9\u9635\u7684\u884c\u5217\u5f0f\u4ee5\u53ca\u5982\u4f55\u53cd\u8f6c\u6b64\u7c7b\u77e9\u9635\u3002<\/p>\n<h2 class=\"wp-block-heading\">\u4ec0\u4e48\u662f\u6807\u91cf\u77e9\u9635\uff1f<\/h2>\n<p class=\"has-background\" style=\"background-color:#dff6ff\"><strong>\u6807\u91cf\u77e9\u9635<\/strong>\u662f\u5bf9<a href=\"https:\/\/mathority.org\/cn\/\u5bf9\u89d2\u77e9\u9635\/\"><span style=\"text-decoration: underline;\">\u89d2\u77e9\u9635<\/span><\/a>\uff0c\u5176\u4e2d\u4e3b\u5bf9\u89d2\u7ebf\u4e0a\u7684\u6240\u6709\u503c\u90fd\u76f8\u7b49\u3002<\/p>\n<p>\u8fd9\u662f\u6807\u91cf\u77e9\u9635\u7684\u5b9a\u4e49\uff0c\u4f46\u6211\u786e\u4fe1\u901a\u8fc7\u793a\u4f8b\u53ef\u4ee5\u66f4\u597d\u5730\u7406\u89e3\u5b83\uff1a\ud83d\ude09<\/p>\n<h2 class=\"wp-block-heading\">\u6807\u91cf\u6570\u7ec4\u7684\u793a\u4f8b<\/h2>\n<p class=\"has-text-align-center has-text-color has-medium-font-size\" style=\"color:#1976d2\"><span style=\"text-decoration: underline;\">2\u00d72 \u9636\u6807\u91cf\u77e9\u9635\u7684\u793a\u4f8b<\/span><\/p>\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/exemple-de-matrice-scalaire-de-dimension-22152-1.webp\" alt=\"\u7ef4\u5ea6\u4e3a 2x2 \u7684\u6807\u91cf\u77e9\u9635\u7684\u793a\u4f8b\" class=\"wp-image-1910\" width=\"80\" height=\"80\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<\/div>\n<p class=\"has-text-align-center has-text-color has-medium-font-size\" style=\"color:#1976d2\"> <span style=\"text-decoration: underline;\">3\u00d73 \u6807\u91cf\u77e9\u9635\u7684\u793a\u4f8b<\/span><\/p>\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/exemple-de-matrice-scalaire-3-dimensionnelle-3-1.webp\" alt=\"\u7ef4\u5ea6\u4e3a 3x3 \u7684\u6807\u91cf\u77e9\u9635\u7684\u793a\u4f8b\" class=\"wp-image-1911\" width=\"116\" height=\"124\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<\/div>\n<p class=\"has-text-align-center has-text-color has-medium-font-size\" style=\"color:#1976d2\"><span style=\"text-decoration: underline;\">\u5927\u5c0f\u4e3a 4\u00d74 \u7684\u6807\u91cf\u77e9\u9635\u7684\u793a\u4f8b<\/span><\/p>\n<div class=\"wp-block-image\">\n<figure class=\"aligncenter size-large is-resized\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/uploads\/2023\/07\/exemple-de-matrice-scalaire-de-dimension-42154-1.webp\" alt=\"\u7ef4\u5ea6\u4e3a 4x4 \u7684\u6807\u91cf\u77e9\u9635\u7684\u793a\u4f8b\" class=\"wp-image-1912\" width=\"218\" height=\"146\" srcset=\"\" sizes=\"auto, \"><\/figure>\n<\/div>\n<h2 class=\"wp-block-heading\">\u6807\u91cf\u77e9\u9635\u7684\u6027\u8d28<\/h2>\n<p>\u6807\u91cf\u77e9\u9635\u4e5f\u662f\u4e00\u4e2a\u5bf9\u89d2\u77e9\u9635\uff0c\u6240\u4ee5\u4f60\u4f1a\u770b\u5230\u5b83\u7ee7\u627f\u4e86\u8fd9\u4e2a\u77e9\u9635\u7c7b\u7684\u8bb8\u591a\u7279\u6027\uff1a<\/p>\n<ul>\n<li>\u6240\u6709\u6807\u91cf\u77e9\u9635\u4e5f\u662f<a href=\"https:\/\/mathority.org\/cn\/\u5bf9\u79f0\u77e9\u9635\u793a\u4f8b\u548c\u6027\u8d28\/\">\u5bf9\u79f0\u77e9\u9635<\/a>\u3002<\/li>\n<\/ul>\n<ul>\n<li>\u6807\u91cf\u77e9\u9635\u65e2\u662f<a href=\"https:\/\/mathority.org\/cn\/\u4e0a\u4e0b\u4e09\u89d2\u77e9\u9635\/\">\u4e0a\u4e09\u89d2\u77e9\u9635\u53c8\u662f\u4e0b\u4e09\u89d2\u77e9\u9635<\/a>\u3002<\/li>\n<\/ul>\n<ul>\n<li><a href=\"https:\/\/mathority.org\/cn\">\u5355\u4f4d\u77e9\u9635<\/a>\u662f\u6807\u91cf\u77e9\u9635\u3002<\/li>\n<\/ul>\n<ul>\n<li>\u4efb\u4f55\u6807\u91cf\u77e9\u9635\u90fd\u53ef\u4ee5\u901a\u8fc7\u5355\u4f4d\u77e9\u9635\u548c\u6807\u91cf\u6570\u7684\u4e58\u79ef\u83b7\u5f97\u3002<\/li>\n<\/ul>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-b77f7d177c2769b0847de258adfd1386_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"4 \\cdot \\begin{pmatrix} 1 &amp; 0 &amp; 0 \\\\[1.1ex] 0 &amp; 1 &amp; 0 \\\\[1.1ex] 0 &amp; 0 &amp; 1 \\end{pmatrix} = \\begin{pmatrix} 4 &amp; 0 &amp; 0 \\\\[1.1ex] 0 &amp; 4 &amp; 0 \\\\[1.1ex] 0 &amp; 0 &amp; 4 \\end{pmatrix}\" title=\"Rendered by QuickLaTeX.com\" height=\"85\" width=\"222\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<ul>\n<li><a href=\"https:\/\/mathority.org\/cn\/\u96f6\u77e9\u9635\/\">\u96f6\u77e9\u9635<\/a>\u4e5f\u662f\u6807\u91cf\u77e9\u9635\u3002<\/li>\n<\/ul>\n<ul>\n<li>\u6807\u91cf\u77e9\u9635\u7684\u7279\u5f81\u503c\uff08\u6216\u7279\u5f81\u503c\uff09\u662f\u5176\u4e3b\u5bf9\u89d2\u7ebf\u7684\u5143\u7d20\u3002\u56e0\u6b64\uff0c\u5b83\u4eec\u7684\u7279\u5f81\u503c\u5c06\u59cb\u7ec8\u76f8\u540c\uff0c\u5e76\u4e14\u4f1a\u91cd\u590d\u4e0e\u77e9\u9635\u7ef4\u6570\u4e00\u6837\u591a\u7684\u6b21\u6570\u3002<\/li>\n<\/ul>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-2513b8d4aeb6d932d9870934102a1637_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\begin{pmatrix} 8 &amp; 0 &amp; 0 \\\\[1.1ex] 0 &amp; 8 &amp; 0 \\\\[1.1ex] 0 &amp; 0 &amp; 8 \\end{pmatrix} \\longrightarrow \\ \\lambda = 8 \\ ; \\ \\lambda = 8 \\ ; \\ \\lambda = 8\" title=\"Rendered by QuickLaTeX.com\" height=\"85\" width=\"298\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<ul>\n<li>\u4e00\u4e2a\u6807\u91cf\u77e9\u9635\u7684\u4f34\u968f\u662f\u53e6\u4e00\u4e2a\u6807\u91cf\u77e9\u9635\u3002\u800c\u4e14\uff0c\u9644\u52a0\u77e9\u9635\u7684\u4e3b\u5bf9\u89d2\u7ebf\u7684\u503c\u5c06\u59cb\u7ec8\u662f\u539f\u59cb\u77e9\u9635\u7684\u503c\u63d0\u5347<em>\u5230\u77e9\u9635 &#8211; 1 \u7684\u9636\u6570<\/em>\u3002<\/li>\n<\/ul>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-1f7e94cc5a528abace04016dc263c8f9_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle A=\\begin{pmatrix} 5 &amp; 0 &amp; 0 \\\\[1.1ex] 0 &amp; 5 &amp; 0 \\\\[1.1ex] 0 &amp; 0 &amp; 5 \\end{pmatrix} \\longrightarrow \\text{Adj}(A)=\\begin{pmatrix} 5^{3-1} &amp; 0 &amp; 0 \\\\[1.1ex] 0 &amp; 5^{3-1} &amp; 0 \\\\[1.1ex] 0 &amp; 0 &amp; 5^{3-1} \\end{pmatrix}= \\begin{pmatrix} 25 &amp; 0 &amp; 0 \\\\[1.1ex] 0 &amp; 25 &amp; 0 \\\\[1.1ex] 0 &amp; 0 &amp; 25 \\end{pmatrix}\" title=\"Rendered by QuickLaTeX.com\" height=\"85\" width=\"546\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<h2 class=\"wp-block-heading\">\u6807\u91cf\u77e9\u9635\u7684\u8fd0\u7b97<\/h2>\n<p>\u6807\u91cf\u77e9\u9635\u5728\u7ebf\u6027\u4ee3\u6570\u4e2d\u5982\u6b64\u5e7f\u6cdb\u4f7f\u7528\u7684\u539f\u56e0\u4e4b\u4e00\u662f\u5b83\u4eec\u5141\u8bb8\u60a8\u8f7b\u677e\u5730\u6267\u884c\u8ba1\u7b97\u3002\u8fd9\u5c31\u662f\u4e3a\u4ec0\u4e48\u5b83\u4eec\u5728\u6570\u5b66\u4e2d\u5982\u6b64\u91cd\u8981\u3002<\/p>\n<p>\u90a3\u4e48\u8ba9\u6211\u4eec\u770b\u770b\u4e3a\u4ec0\u4e48\u4f7f\u7528\u8fd9\u79cd\u7c7b\u578b\u7684\u65b9\u9635\u8fdb\u884c\u8ba1\u7b97\u5982\u6b64\u5bb9\u6613\uff1a<\/p>\n<h3 class=\"wp-block-heading\">\u6807\u91cf\u77e9\u9635\u7684\u52a0\u6cd5\u548c\u51cf\u6cd5<\/h3>\n<p>\u4e24\u4e2a\u6807\u91cf\u77e9\u9635\u76f8\u52a0\uff08\u6216\u76f8\u51cf\uff09\u975e\u5e38\u7b80\u5355\uff1a\u53ea\u9700\u76f8\u52a0\uff08\u6216\u76f8\u51cf\uff09\u4e3b\u5bf9\u89d2\u7ebf\u4e0a\u7684\u6570\u5b57\u5373\u53ef\u3002\u4f8b\u5982\uff1a<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-761de4b4c9bdbbc835b366b21d8cfc2d_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\begin{pmatrix} 4 &amp; 0 &amp; 0 \\\\[1.1ex] 0 &amp; 4 &amp; 0 \\\\[1.1ex] 0 &amp; 0 &amp; 4 \\end{pmatrix} +\\begin{pmatrix} 3 &amp; 0 &amp; 0 \\\\[1.1ex] 0 &amp; 3 &amp; 0 \\\\[1.1ex] 0 &amp; 0 &amp; 3 \\end{pmatrix} = \\begin{pmatrix} 7&amp; 0 &amp; 0 \\\\[1.1ex] 0 &amp; 7 &amp; 0 \\\\[1.1ex] 0 &amp; 0 &amp; 7 \\end{pmatrix}\" title=\"Rendered by QuickLaTeX.com\" height=\"85\" width=\"306\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<h3 class=\"wp-block-heading\">\u6807\u91cf\u77e9\u9635\u4e58\u6cd5<\/h3>\n<p>\u4e0e\u52a0\u6cd5\u548c\u51cf\u6cd5\u7c7b\u4f3c\uff0c\u8981\u6c42\u89e3\u4e24\u4e2a\u6807\u91cf\u77e9\u9635\u4e4b\u95f4\u7684\u4e58\u6cd5\u6216\u77e9\u9635\u4e58\u79ef\uff0c\u53ea\u9700\u5c06\u5b83\u4eec\u4e4b\u95f4\u7684\u5bf9\u89d2\u7ebf\u5143\u7d20\u76f8\u4e58\u5373\u53ef\u3002\u4f8b\u5982\uff1a<\/p>\n<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-d30acbf9c6ad31625f8253549e659b02_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\\displaystyle \\begin{pmatrix} 2 &amp; 0 &amp; 0 \\\\[1.1ex] 0 &amp; 2 &amp; 0 \\\\[1.1ex] 0 &amp; 0 &amp; 2 \\end{pmatrix} \\cdot\\begin{pmatrix} 6 &amp; 0 &amp; 0 \\\\[1.1ex] 0 &amp; 6 &amp; 0 \\\\[1.1ex] 0 &amp; 0 &amp; 6 \\end{pmatrix} = \\begin{pmatrix} 12 &amp; 0 &amp; 0 \\\\[1.1ex] 0 &amp; 12 &amp; 0 \\\\[1.1ex] 0 &amp; 0 &amp; 12 \\end{pmatrix}\" title=\"Rendered by QuickLaTeX.com\" height=\"85\" width=\"323\" style=\"vertical-align: 0px;\"><\/p>\n<\/p>\n<h3 class=\"wp-block-heading\">\u6807\u91cf\u77e9\u9635\u7684\u5e42<\/h3>\n<p>\u8ba1\u7b97\u6807\u91cf\u77e9\u9635\u7684\u5e42\u4e5f\u975e\u5e38\u7b80\u5355\uff1a\u60a8\u5fc5\u987b\u5c06\u5bf9\u89d2\u7ebf\u7684\u6bcf\u4e2a\u5143\u7d20\u63d0\u9ad8\u5230\u6307\u6570\u3002\u4f8b\u5982\uff1a<\/p>\n<pre class=\"ql-errors\"> *** QuickLaTeX cannot compile formula:\n\\displaystyle\\left. \\begin{pmatrix} 2 &amp; 0 &amp; 0 \\\\[1.1ex] 0 &amp; 2 &amp; 0 \\\\[1.1ex] 0 &amp; 0 &amp; 2 \\end{pmatrix}\\right.^4=\\begin{pmatrix} 2^ 4 &amp; 0 &amp; 0 \\\\[1.1ex] 0 &amp; 2^\n\n*** Error message:\nMissing $ inserted.\nleading text: \\displaystyle\nMissing { inserted.\nleading text: \\end{document}\n\\begin{pmatrix} on input line 9 ended by \\end{document}.\nleading text: \\end{document}\nImproper \\prevdepth.\nleading text: \\end{document}\nMissing $ inserted.\nleading text: \\end{document}\nMissing } inserted.\nleading text: \\end{document}\nMissing } inserted.\nleading text: \\end{document}\nMissing \\cr inserted.\nleading text: \\end{document}\nMissing $ inserted.\nleading text: \\end{document}\nYou can't use `\\end' in internal vertical mode.\nleading text: \\end{document}\n\\begin{pmatrix} on input line 9 ended by \\end{document}.\nleading text: \\end{document}\nMissing } inserted.\nleading text: \\end{document}\nMissing \\right. inserted.\nleading text: \\end{document}\n\n<\/pre>\n<p> &amp; 0 \\\\[1.1ex] 0 &amp; 0 &amp; 2^4 \\end{pmatrix}= \\begin{pmatrix} 16 &amp; 0 &amp; 0 \\\\[1.1ex] 0 &amp; 16 &amp; 0 \\\\[1.1ex] 0 &amp; 0 \u548c 16 \\end{pmatrix}<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-ca97d1162704371c21b308778890f436_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"\n\n<div class=&quot;adsb30&quot; style=&quot; margin:px; text-align:&quot;><\/div>\n<h2 class=&quot;wp-block-heading&quot;> D\u00e9terminant d&#8217;une matrice scalaire<\/h2>\n<p> Calculer le <strong>d\u00e9terminant d&#8217;une matrice scalaire<\/strong> revient \u00e0 r\u00e9soudre le d\u00e9terminant d&#8217;une matrice diagonale : le r\u00e9sultat est le produit des \u00e9l\u00e9ments sur la diagonale principale.&#8221; title=&#8221;Rendered by QuickLaTeX.com&#8221; height=&#8221;106&#8243; width=&#8221;582&#8243; style=&#8221;vertical-align: -4px;&#8221;><\/p>\n<p> \\displaystyle \\text{det}(A)= \\prod_{i =1}^n a_i<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-7b3ddf4b77e65a9bd0387f51b7bcaa40_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\" Regardez l'exercice r\u00e9solu suivant dans lequel on trouve le d\u00e9terminant d'une matrice scalaire en multipliant les \u00e9l\u00e9ments de sa diagonale principale :\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"1099\" style=\"vertical-align: -4px;\"><\/p>\n<p> \\displaystyle \\begin{vmatrix} 7 &amp; 0 &amp; 0 \\\\[1.1ex] 0 &amp; 7 &amp; 0 \\\\[1.1ex] 0 &amp; 0 &amp; 7 \\end{vmatrix} = 7 \\cdot 7 \\cdot 7 = \\bm {343}<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-773692a573846f155d4c92f1e9075001_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\" En fait, puisque tous les \u00e9l\u00e9ments de la diagonale principale d'une matrice scalaire sont toujours \u00e9gaux, pour trouver le r\u00e9sultat du d\u00e9terminant, il suffit d'augmenter le num\u00e9ro de la diagonale principale du nombre de fois qu'elle est r\u00e9p\u00e9t\u00e9e. Par cons\u00e9quent, l'exercice pr\u00e9c\u00e9dent peut \u00e9galement \u00eatre r\u00e9solu de la mani\u00e8re suivante :\" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"2411\" style=\"vertical-align: -4px;\"><\/p>\n<p> \\displaystyle \\begin{vmatrix} 7 &amp; 0 &amp; 0 \\\\[1.1ex] 0 &amp; 7 &amp; 0 \\\\[1.1ex] 0 &amp; 0 &amp; 7 \\end{vmatrix} = 7^3= \\bm{343}<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-d24f9aa91fc9fe8ed74f705f83be3b32_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\" D\u00e9montrer ce th\u00e9or\u00e8me est tr\u00e8s simple : il suffit de calculer le d\u00e9terminant d'une matrice scalaire par blocs (ou cofacteurs). Vous trouverez ci-dessous la <strong>d\u00e9monstration<\/strong> de la formule utilisant une matrice scalaire g\u00e9n\u00e9rique :&#8221; title=&#8221;Rendered by QuickLaTeX.com&#8221; height=&#8221;62&#8243; width=&#8221;1060&#8243; style=&#8221;vertical-align: -4px;&#8221;><\/p>\n<p> \\begin{\u5bf9\u9f50} \\begin{vmatrix} a &amp; 0 &amp; 0 \\\\[1.1ex] 0 &amp; a &amp; 0 \\\\[1.1ex] 0 &amp; 0 &amp; a \\end{vmatrix}&amp; = a \\cdot \\begin{ vmatrix} a &amp; 0 \\\\[1.1ex] 0 &amp; a \\end{vmatrix} \u2013 0 \\cdot \\begin{vmatrix} 0 &amp; 0 \\\\[1.1ex] 0 &amp; a \\end{vmatrix} + 0 \\cdot \\\u5f00\u59cb{vmatrix} 0 &amp; a \\\\[1.1ex] 0 &amp; 0 \\end{vmatrix} \\\\[2ex] &amp; =a \\cdot (a\\cdot a) \u2013 0 \\cdot 0 + 0 \\cdot 0 \\\\[ 2ex] &amp; = a \\cdot a \\cdot a \\\\[2ex] &amp; = a^3 \\end{\u5bf9\u9f50}<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-dc127c7827a5f62c565b8ada378986a8_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\" Dans ce cas \u00e7a donne\" title=\"Rendered by QuickLaTeX.com\" height=\"13\" width=\"149\" style=\"vertical-align: -1px;\"><\/p>\n<p>\u4e00\u4e2a^3<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-49f5afdd3e1e9918f5323139662a2138_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\"car la matrice est d'ordre 3, mais il faut toujours l'\u00e9lever \u00e0 l'ordre de la matrice. \n\n<div class=&quot;adsb30&quot; style=&quot; margin:12px; text-align:center&quot;>\n<div id=&quot;ezoic-pub-ad-placeholder-118&quot;><\/div>\n<\/div>\n<h2 class=&quot;wp-block-heading&quot;> Inverser une matrice scalaire<\/h2>\n<p> Une matrice scalaire <strong>est inversible si, et seulement si, tous les \u00e9l\u00e9ments de la diagonale principale sont diff\u00e9rents de 0<\/strong> . Dans ce cas on dit que la matrice scalaire est une matrice r\u00e9guli\u00e8re. De plus, l&#8217;inverse d&#8217;une matrice scalaire sera toujours une autre matrice scalaire avec les <strong>inverses<\/strong> de la diagonale principale :&#8221; title=&#8221;Rendered by QuickLaTeX.com&#8221; height=&#8221;174&#8243; width=&#8221;1250&#8243; style=&#8221;vertical-align: -5px;&#8221;><\/p>\n<p> \\displaystyle A= \\begin{pmatrix} 9 &amp; 0 &amp; 0 \\\\[1.1ex] 0 &amp; 9 &amp; 0 \\\\[1.1ex] 0 &amp; 0 &amp; 9 \\end{pmatrix} \\ \\longrightarrow \\ A^{-1 }=\\begin{pmatrix} \\frac{1}{9} &amp; 0 &amp; 0 \\\\[1.1ex] 0 &amp; \\frac{1}{9} &amp; 0 \\\\[1.1ex] 0 &amp; 0 &amp; \\frac{ 1}{9} \\end{pmatrix}<\/p>\n<p class=\"has-text-align-center\"><img decoding=\"async\" loading=\"lazy\" src=\"https:\/\/mathority.org\/wp-content\/ql-cache\/quicklatex.com-9eaf19f57b0cbab7f60c5c1dc0ec45eb_l3.png\" class=\"ql-img-inline-formula quicklatex-auto-format\" alt=\" D'autre part, de la caract\u00e9ristique pr\u00e9c\u00e9dente, on peut d\u00e9duire que le d\u00e9terminant d'une matrice scalaire invers\u00e9e est le r\u00e9sultat de la multiplication des inverses de la diagonale principale : \" title=\"Rendered by QuickLaTeX.com\" height=\"18\" width=\"1373\" style=\"vertical-align: -4px;\"><\/p>\n<p> \\displaystyle B= \\begin{pmatrix} 2 &amp; 0 &amp; 0 \\\\[1.1ex] 0 &amp; 2 &amp; 0 \\\\[1.1ex] 0 &amp; 0 &amp; 2 \\end{pmatrix} \\displaystyle\\left| B^{-1}\\right|=\\cfrac{1}{2} \\cdot \\cfrac{1}{2} \\cdot \\cfrac{1}{2}=\\cfrac{1}{8} = $0.125<\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u5728\u6b64\u9875\u9762\u4e0a\uff0c\u60a8\u5c06\u627e\u5230\u4ec0\u4e48\u662f\u6807\u91cf\u77e9\u9635\u4ee5\u53ca\u6807\u91cf\u77e9\u9635\u7684\u51e0\u4e2a\u793a\u4f8b\uff0c\u4ee5\u4fbf\u5b8c\u5168\u7406\u89e3\u5b83\u3002\u6b64\u5916\uff0c\u60a8\u5c06\u80fd\u591f\u770b\u5230\u6807\u91cf\u77e9\u9635\u7684\u6240\u6709\u5c5e\u6027 &hellip;<\/p>\n<p class=\"read-more\"> <a class=\"\" href=\"https:\/\/mathority.org\/cn\/%e6%a0%87%e9%87%8f%e7%9f%a9%e9%98%b5\/\"> <span class=\"screen-reader-text\">\u6807\u91cf\u77e9\u9635<\/span> \u67e5\u770b\u5168\u6587 &raquo;<\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"","footnotes":""},"categories":[31],"tags":[],"class_list":["post-303","post","type-post","status-publish","format-standard","hentry","category-31"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v21.2 - 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