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id=\"%E5%89%8D%E8%A8%80\">\u524d\u8a00<\/h2>\n<p>\u524d\u9762\u6211\u4eec\u901a\u8fc7\u51e0\u4f55\u5173\u7cfb\u5f15\u5165\u4e86\u77e9\u9635\u4ee5\u53ca\u77e9\u9635\u4e58\u6cd5&#xff08;\u4f20\u9001\u95e8&#xff1a;https:\/\/blog.csdn.net\/weixin_38357164\/article\/details\/158415735?fromshare&#061;blogdetail&amp;sharetype&#061;blogdetail&amp;sharerId&#061;158415735&amp;sharerefer&#061;PC&amp;sharesource&#061;weixin_38357164&amp;sharefrom&#061;from_link&#xff09;&#xff0c;\u8fd9\u4e00\u7bc7\u5185\u5bb9\u6211\u4eec\u4e3b\u8981\u8ba4\u8bc6\u4e00\u4e0b\u77e9\u9635\u548c\u77e9\u9635\u7684\u8ba1\u7b97&#xff0c;\u540e\u7eed\u5c06\u6301\u7eed\u66f4\u65b0\u5b66\u4e60\u5185\u5bb9&#xff0c;\u6b22\u8fce\u6709\u5174\u8da3\u7684\u670b\u53cb\u4e00\u8d77\u5b66\u4e60\u5171\u540c\u8fdb\u6b65&#xff01;~~~\u3002<\/p>\n<h2 id=\"%E7%9F%A9%E9%98%B5%E5%9F%BA%E7%A1%80\">\u77e9\u9635\u57fa\u7840<\/h2>\n<h3 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id=\"%E7%9F%A9%E9%98%B5%E7%9A%84%E8%A1%A8%E7%A4%BA%E6%B3%95\">\u77e9\u9635\u7684\u8868\u793a\u6cd5<\/h3>\n<p>\u4e00\u4e2a\u77e9\u9635\u901a\u5e38\u7528\u5706\u62ec\u53f7\u6216\u65b9\u62ec\u53f7\u5c06\u6570\u5b57\u9635\u5217\u62ec\u8d77\u6765\u3002\u624b\u5199\u7684\u65f6\u5019\u4e00\u5b9a\u7528\u5706\u62ec\u5f27&#xff0c;\u5370\u5237\u4f53\u7684\u65f6\u5019\u7528\u4e00\u822c\u4f1a\u7528\u4e2d\u62ec\u5f27\u3002\u901a\u5e38\u7528\u5927\u5199\u7c97\u4f53\u5b57\u6bcd&#xff08;\u5982\u00a0A\u3001B&#xff09;\u6765\u8868\u793a\u3002\u4f8b\u5982\u77e9\u9635\u00a0A\u00a0\u662f\u4e00\u4e2a m\u00d7n\u77e9\u9635&#xff08;m\u884cn\u5217&#xff09;&#xff0c;\u5982\u4e0b\u6240\u793a&#xff1a;<\/p>\n<p><img decoding=\"async\" alt=\"$A &#061; \\\\begin{pmatrix} a_{11} &amp; a_{12} &amp; \\\\cdots &amp; a_{1n} \\\\\\\\ a_{21} &amp; a_{22} &amp; \\\\cdots &amp; a_{2n} \\\\\\\\ \\\\vdots &amp; \\\\vdots &amp; \\\\cdots &amp; \\\\vdots \\\\\\\\ a_{m1} &amp; a_{m2} &amp; \\\\cdots &amp; a_{mn} \\\\end{pmatrix}$\" 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id=\"%E7%9F%A9%E9%98%B5%E7%9A%84%E5%85%83%E7%B4%A0\">\u77e9\u9635\u7684\u5143\u7d20<\/h3>\n<p>\u77e9\u9635\u4e2d\u7684\u6bcf\u4e2a\u6570\u5b57\u79f0\u4e3a\u77e9\u9635\u7684\u5143\u7d20&#xff08;\u6216\u9879&#xff09;\u3002\u6211\u4eec\u901a\u5e38\u4f7f\u7528\u77e9\u9635\u540d\u79f0\u7684\u5c0f\u5199\u5b57\u6bcd&#xff0c;\u5e76\u52a0\u4e0a\u4e24\u4e2a\u4e0b\u6807\u6765\u8868\u793a\u5143\u7d20\u7684\u4f4d\u7f6e\u3002<\/p>\n<ul>\n<li>\n<p>\u7b2c\u4e00\u4e2a\u4e0b\u6807\u8868\u793a\u884c\u53f7\u3002<\/p>\n<\/li>\n<li>\n<p>\u7b2c\u4e8c\u4e2a\u4e0b\u6807\u8868\u793a\u5217\u53f7\u3002<\/p>\n<\/li>\n<\/ul>\n<p>\u4f8b\u5982&#xff0c;\u5bf9\u4e8e\u77e9\u9635\u00a0A&#xff0c;\u5143\u7d20\u00a0aij\u200b\u00a0\u8868\u793a\u4f4d\u4e8e\u7b2c i \u884c\u3001\u7b2c j \u5217\u7684\u5143\u7d20\u3002<\/p>\n<ul>\n<li>\n<p><img decoding=\"async\" alt=\"a_{11}\" class=\"mathcode\" src=\"https:\/\/www.wsisp.com\/helps\/wp-content\/uploads\/2026\/02\/20260227143101-69a1aaa5e2e5f.png\" \/>&#061;1&#xff08;\u7b2c1\u884c\u7b2c1\u5217&#xff09;<\/p>\n<\/li>\n<li>\n<p><img decoding=\"async\" alt=\"a_{12}\" class=\"mathcode\" src=\"https:\/\/www.wsisp.com\/helps\/wp-content\/uploads\/2026\/02\/20260227143102-69a1aaa60140c.png\" \/>\u200b&#061;2&#xff08;\u7b2c1\u884c\u7b2c2\u5217&#xff09;<\/p>\n<\/li>\n<li>\n<p><img decoding=\"async\" alt=\"a_{23}\" class=\"mathcode\" src=\"https:\/\/www.wsisp.com\/helps\/wp-content\/uploads\/2026\/02\/20260227143102-69a1aaa611496.png\" \/>&#061;6&#xff08;\u7b2c2\u884c\u7b2c3\u5217&#xff09;<\/p>\n<\/li>\n<\/ul>\n<p>\u56e0\u6b64&#xff0c;\u4e00\u4e2a\u4e00\u822c\u7684\u00a0m\u00d7n\u00a0\u77e9\u9635\u53ef\u4ee5\u5199\u6210<\/p>\n<p><img decoding=\"async\" alt=\"$A &#061; \\\\begin{pmatrix} a_{11} &amp; a_{12} &amp; \\\\cdots &amp; a_{1n} \\\\\\\\ a_{21} &amp; a_{22} &amp; \\\\cdots &amp; a_{2n} \\\\\\\\ \\\\vdots &amp; \\\\vdots &amp; \\\\cdots &amp; \\\\vdots \\\\\\\\ a_{m1} &amp; a_{m2} &amp; \\\\cdots &amp; a_{mn} \\\\end{pmatrix}$\" class=\"mathcode\" src=\"https:\/\/www.wsisp.com\/helps\/wp-content\/uploads\/2026\/02\/20260227143101-69a1aaa5ba53e.png\" \/><\/p>\n<h3 id=\"%E7%89%B9%E6%AE%8A%E7%9A%84%E7%9F%A9%E9%98%B5\">\u7279\u6b8a\u7684\u77e9\u9635<\/h3>\n<h4 id=\"%E8%A1%8C%E7%9F%A9%E9%98%B5\">\u884c\u77e9\u9635<\/h4>\n<p>\u53ea\u6709\u4e00\u884c\u7684\u77e9\u9635&#xff08;1\u00d7n\u77e9\u9635&#xff09;\u3002\u4f8b\u5982\u00a0[1\u00a02\u00a03]&#xff0c;\u5199\u4e3a&#xff1a;<img decoding=\"async\" alt=\"(a_{11}\\\\quad a_{12}\\\\quad \\\\cdots\\\\quad a_{1n})\" class=\"mathcode\" src=\"https:\/\/www.wsisp.com\/helps\/wp-content\/uploads\/2026\/02\/20260227143102-69a1aaa61eca8.png\" \/><\/p>\n<h4 id=\"%E5%88%97%E7%9F%A9%E9%98%B5\">\u5217\u77e9\u9635<\/h4>\n<p>\u53ea\u6709\u4e00\u5217\u7684\u77e9\u9635&#xff08;m\u00d71 \u77e9\u9635&#xff09;\u3002\u4f8b\u5982\u00a0<img decoding=\"async\" alt=\"\\\\begin{bmatrix} 1 \\\\\\\\ 2 \\\\\\\\ 3 \\\\end{bmatrix}\" class=\"mathcode\" src=\"https:\/\/www.wsisp.com\/helps\/wp-content\/uploads\/2026\/02\/20260227143102-69a1aaa62c25f.png\" \/>&#xff0c;\u5199\u4e3a&#xff1a;<img decoding=\"async\" alt=\"\\\\begin{pmatrix} a_{11} \\\\\\\\ a_{21} \\\\\\\\ \\\\vdots \\\\\\\\ a_{m1} \\\\end{pmatrix}\" class=\"mathcode\" src=\"https:\/\/www.wsisp.com\/helps\/wp-content\/uploads\/2026\/02\/20260227143102-69a1aaa638609.png\" \/><\/p>\n<h4 id=\"%E6%96%B9%E9%98%B5\">\u65b9\u9635<\/h4>\n<p>\u5f53m&#061;n\u65f6&#xff0c;\u5373\u77e9\u9635\u7684\u884c\u6570\u4e0e\u5217\u6570\u76f8\u540c\u65f6&#xff0c;\u79f0\u77e9\u9635\u4e3a\u65b9\u9635\u3002<\/p>\n<h5 id=\"%E4%B8%BB%E5%AF%B9%E8%A7%92%E7%BA%BF\">\u4e3b\u5bf9\u89d2\u7ebf<\/h5>\n<p>\u53ea\u6709\u65b9\u9635\u624d\u6709\u4e3b\u5bf9\u89d2\u7ebf \u3002\u4ece\u77e9\u9635\u5de6\u4e0a\u89d2\u5230\u53f3\u4e0b\u89d2&#xff0c;\u7531\u6240\u6709\u884c\u4e0b\u6807 &#061; \u5217\u4e0b\u6807\u7684\u5143\u7d20\u7ec4\u6210\u7684\u5bf9\u89d2\u7ebf\u3002<\/p>\n<p><img decoding=\"async\" alt=\"A_{n \\\\times n} &#061; \\\\begin{pmatrix} a_{11} &amp; a_{12} &amp; \\\\cdots &amp; a_{1n} \\\\\\\\ a_{21} &amp; a_{22} &amp; \\\\cdots &amp; a_{2n} \\\\\\\\ \\\\vdots &amp; \\\\vdots &amp; \\\\ddots &amp; \\\\vdots \\\\\\\\ a_{n1} &amp; a_{n2} &amp; \\\\cdots &amp; a_{nn} \\\\end{pmatrix}\" class=\"mathcode\" src=\"https:\/\/www.wsisp.com\/helps\/wp-content\/uploads\/2026\/02\/20260227143102-69a1aaa644efb.png\" \/><\/p>\n<h5 id=\"%E6%96%9C%E5%AF%B9%E8%A7%92%E7%BA%BF\">\u659c\u5bf9\u89d2\u7ebf<\/h5>\n<p>\u4ece\u77e9\u9635\u7684\u53f3\u4e0a\u89d2&#xff08;\u7b2c 1 \u884c\u7b2c n \u5217&#xff09;\u5ef6\u4f38\u5230\u5de6\u4e0b\u89d2&#xff08;\u7b2c n \u884c\u7b2c 1 \u5217&#xff09;\u3002\u659c\u5bf9\u89d2\u7ebf\u4e0a\u7684\u5143\u7d20\u4f4d\u7f6e\u6ee1\u8db3&#xff1a;\u884c\u4e0b\u6807 &#043; \u5217\u4e0b\u6807 &#061; n &#043; 1\u3002\u5373&#xff1a;<img decoding=\"async\" alt=\"a_{i,n&#043;1-i} \\\\quad (i &#061; 1, 2, \\\\dots, n)\" class=\"mathcode\" src=\"https:\/\/www.wsisp.com\/helps\/wp-content\/uploads\/2026\/02\/20260227143102-69a1aaa654aa6.png\" \/>\u3002<\/p>\n<p><img decoding=\"async\" alt=\"$A_{n \\\\times n} &#061; \\\\begin{pmatrix} a_{11} &amp; a_{12} &amp; \\\\cdots &amp; a_{1(n-1)} &amp; a_{1n} \\\\\\\\ a_{21} &amp; a_{22} &amp; \\\\cdots &amp; a_{2(n-1)} &amp; a_{2n} \\\\\\\\ \\\\vdots &amp; \\\\vdots &amp; \\\\ddots &amp; \\\\vdots &amp; \\\\vdots \\\\\\\\ a_{(n-1)1} &amp; a_{(n-1)2} &amp; \\\\cdots &amp; a_{(n-1)(n-1)} &amp; a_{(n-1)n} \\\\\\\\ a_{n1} &amp; a_{n2} &amp; \\\\cdots &amp; a_{n(n-1)} &amp; a_{nn} \\\\end{pmatrix}$\" class=\"mathcode\" src=\"https:\/\/www.wsisp.com\/helps\/wp-content\/uploads\/2026\/02\/20260227143102-69a1aaa66280f.png\" \/><\/p>\n<h5 id=\"%E5%8D%95%E4%BD%8D%E9%98%B5\">\u5355\u4f4d\u9635<\/h5>\n<p>\u5b83\u7684\u4e3b\u5bf9\u89d2\u7ebf\u4e0a\u7684\u5143\u7d20\u5168\u4e3a 1&#xff0c;\u5176\u4f59\u6240\u6709\u5143\u7d20\u5168\u4e3a 0&#xff0c;\u5c31\u5f97\u5230\u53c8\u4e00\u4e2a\u7279\u6b8a\u7684\u77e9\u9635\u53eb\u505a\u5355\u4f4d\u9635&#xff0c;&#xff0c;\u8bb0\u4e3a <img decoding=\"async\" alt=\"E_n\" class=\"mathcode\" src=\"https:\/\/www.wsisp.com\/helps\/wp-content\/uploads\/2026\/02\/20260227143102-69a1aaa674a27.png\" \/>\u00a0\u6216\u00a0<img decoding=\"async\" alt=\"L_n\" class=\"mathcode\" src=\"https:\/\/www.wsisp.com\/helps\/wp-content\/uploads\/2026\/02\/20260227143102-69a1aaa680fd9.png\" \/>\u3002<\/p>\n<h6 id=\"%E5%8D%95%E4%BD%8D%E9%98%B5%E6%80%A7%E8%B4%A8\">\u5355\u4f4d\u9635\u6027\u8d28<\/h6>\n<p>\u5bf9\u4efb\u610f\u53ef\u4e58\u77e9\u9635 A&#xff0c;\u5219\u6709&#xff1a;<img decoding=\"async\" alt=\"$A E_n &#061; A,\\\\quad E_m A &#061; A$\" class=\"mathcode\" src=\"https:\/\/www.wsisp.com\/helps\/wp-content\/uploads\/2026\/02\/20260227143102-69a1aaa68d2a0.png\" \/><\/p>\n<p>\u8f6c\u7f6e\u4e0d\u53d8&#xff1a;<img decoding=\"async\" alt=\"$E_n^T &#061; E_n$\" class=\"mathcode\" src=\"https:\/\/www.wsisp.com\/helps\/wp-content\/uploads\/2026\/02\/20260227143102-69a1aaa69a78a.png\" \/><\/p>\n<p>\u5e42\u7b49\u6027&#xff1a;<img decoding=\"async\" alt=\"$E_n^k &#061; E_n$\" class=\"mathcode\" src=\"https:\/\/www.wsisp.com\/helps\/wp-content\/uploads\/2026\/02\/20260227143102-69a1aaa6a6d94.png\" \/>\u00a0 &#xff08;\u4efb\u610f\u6b63\u6574\u6570 k&#xff09;\u00a0\u00a0<\/p>\n<h5 id=\"%E6%95%B0%E9%87%8F%E9%98%B5\">\u6570\u91cf\u9635<\/h5>\n<p>\u5b83\u7684\u4e3b\u5bf9\u89d2\u7ebf\u4e0a\u7684\u5143\u7d20\u5168\u4e3a k&#xff0c;\u5176\u4f59\u6240\u6709\u5143\u7d20\u5168\u4e3a 0&#xff0c;\u5c31\u5f97\u5230\u53c8\u4e00\u4e2a\u7279\u6b8a\u7684\u77e9\u9635\u53eb\u505a\u6570\u91cf\u9635<\/p>\n<h5 id=\"%E4%B8%8A%E4%B8%89%E8%A7%92%E7%9F%A9%E9%98%B5\">\u4e0a\u4e09\u89d2\u77e9\u9635<\/h5>\n<p>\u4e3b\u5bf9\u89d2\u7ebf\u4ee5\u4e0b\u7684\u5143\u7d20\u5168\u4e3a\u96f6\u7684\u65b9\u9635&#xff0c;\u5bf9\u4e8e\u4e00\u4e2a\u77e9\u9635\u00a0U&#xff0c;\u5982\u679c\u5f53\u00a0i&gt;j&#xff08;\u5373\u884c\u53f7\u5927\u4e8e\u5217\u53f7&#xff0c;\u4e5f\u5c31\u662f\u4e3b\u5bf9\u89d2\u7ebf\u4ee5\u4e0b\u7684\u5143\u7d20&#xff09;\u65f6&#xff0c;\u6709<img decoding=\"async\" alt=\"u_{ij} &#061; 0\" class=\"mathcode\" src=\"https:\/\/www.wsisp.com\/helps\/wp-content\/uploads\/2026\/02\/20260227143102-69a1aaa6b3d82.png\" \/>&#xff0c;\u90a3\u4e48\u00a0U\u5c31\u662f\u4e00\u4e2a\u4e0a\u4e09\u89d2\u77e9\u9635\u3002<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" alt=\"\" height=\"184\" src=\"https:\/\/www.wsisp.com\/helps\/wp-content\/uploads\/2026\/02\/20260227143102-69a1aaa6c4880.png\" width=\"408\" \/><\/p>\n<h5 id=\"%E4%B8%8B%E4%B8%89%E8%A7%92%E7%9F%A9%E9%98%B5\">\u4e0b\u4e09\u89d2\u77e9\u9635<\/h5>\n<p>\u5bf9\u4e8e\u4e00\u4e2a\u77e9\u9635\u00a0L&#xff0c;\u5982\u679c\u5f53\u00a0i&lt;j&#xff08;\u5373\u884c\u53f7\u5c0f\u4e8e\u5217\u53f7&#xff0c;\u4e5f\u5c31\u662f\u4e3b\u5bf9\u89d2\u7ebf\u4ee5\u4e0a\u7684\u5143\u7d20&#xff09;\u65f6&#xff0c;\u6709\u00a0<img decoding=\"async\" alt=\"l_{ij} &#061; 0\" class=\"mathcode\" src=\"https:\/\/www.wsisp.com\/helps\/wp-content\/uploads\/2026\/02\/20260227143102-69a1aaa6daac2.png\" \/>&#xff0c;\u90a3\u4e48\u00a0LL\u5c31\u662f\u4e00\u4e2a\u4e0b\u4e09\u89d2\u77e9\u9635<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" alt=\"\" height=\"190\" src=\"https:\/\/www.wsisp.com\/helps\/wp-content\/uploads\/2026\/02\/20260227143102-69a1aaa6e9688.png\" width=\"390\" \/><\/p>\n<h4 id=\"%E9%9B%B6%E7%9F%A9%E9%98%B5\">\u96f6\u77e9\u9635<\/h4>\n<p>\u6240\u6709\u5143\u7d20\u90fd\u662f0\u7684\u77e9\u9635&#xff0c;\u96f6\u77e9\u9635\u7528\u5927\u5199\u7684O\u8868\u793a\u3002<\/p>\n<p><img decoding=\"async\" alt=\"$O_{m \\\\times n} &#061; \\\\begin{pmatrix} 0 &amp; \\\\cdots &amp; 0 \\\\\\\\ \\\\vdots &amp; \\\\ddots &amp; \\\\vdots \\\\\\\\ 0 &amp; \\\\cdots &amp; 0 \\\\end{pmatrix}$\" class=\"mathcode\" src=\"2026-02-27vb5cfr5ecnz.png\" \/><\/p>\n<h4 id=\"%E6%A2%AF%E5%BD%A2%E9%98%B5\">\u68af\u5f62\u9635<\/h4>\n<p>\u8bbe<img decoding=\"async\" alt=\"A &#061; (a_{ij})_{m \\\\times n}\" class=\"mathcode\" src=\"2026-02-275s1tv1jtdp5.png\" \/>\u4e3a\u975e\u96f6\u77e9\u9635&#xff0c;\u82e5\u975e\u96f6\u884c(\u5373\u81f3\u5c11\u6709\u4e00\u4e2a\u975e\u96f6\u5143\u7d20\u7684\u884c)\u5168\u5728\u96f6\u884c\u7684\u4e0a\u9762&#xff0c;A\u4e2d\u5404\u975e\u96f6\u884c\u4e2d\u7b2c\u4e00\u4e2a(\u6700\u540e\u4e00\u4e2a)\u975e\u96f6\u5143\u7d20\u524d(\u540e)\u9762\u96f6\u5143\u7d20\u7684\u4e2a\u6570\u968f\u884c\u6570\u589e\u5927\u800c\u589e\u591a(\u51cf\u5c11)&#xff0c;\u5219\u79f0\u4e3a\u4e0a(\u4e0b)\u68af\u5f62\u77e9\u9635\u3002\u7b80\u79f0\u4e3a\u4e0a(\u4e0b)\u68af\u5f62\u9635\u3002<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" alt=\"\" height=\"394\" src=\"2026-02-27sval1svnm0m.png\" width=\"1378\" \/><\/p>\n<p><img loading=\"lazy\" decoding=\"async\" alt=\"\" height=\"406\" src=\"2026-02-27dw1wraz2wce.png\" width=\"1376\" \/><\/p>\n<h2 id=\"%E7%9F%A9%E9%98%B5%E7%9A%84%E8%BF%90%E7%AE%97\">\u77e9\u9635\u7684\u8fd0\u7b97<\/h2>\n<h3 id=\"%E7%9F%A9%E9%98%B5%E7%9B%B8%E7%AD%89\">\u77e9\u9635\u76f8\u7b49<\/h3>\n<p>\u4e24\u4e2a\u77e9\u9635\u00a0A\u00a0\u548c\u00a0B\u00a0\u79f0\u4e3a\u76f8\u7b49&#xff0c;\u8bb0\u4f5c\u00a0A &#061; B&#xff0c;\u5f53\u4e14\u4ec5\u5f53\u5b83\u4eec\u6ee1\u8db3\u4ee5\u4e0b\u4e24\u4e2a\u6761\u4ef6&#xff1a;<\/p>\n<p>\u7ef4\u5ea6\u76f8\u540c&#xff1a;\u77e9\u9635\u00a0A\u00a0\u548c\u00a0B\u00a0\u5fc5\u987b\u6709\u76f8\u540c\u7684\u884c\u6570\u548c\u76f8\u540c\u7684\u5217\u6570&#xff08;\u5373\u540c\u4e3a\u00a0m\u00d7n \u77e9\u9635&#xff09;\u3002<\/p>\n<p>\u5bf9\u5e94\u5143\u7d20\u76f8\u7b49&#xff1a;\u5bf9\u4e8e\u6240\u6709\u7684\u00a0i\u00a0\u548c\u00a0j &#xff08;1\u2264i\u2264m&#xff0c;1\u2264j\u2264n&#xff09;&#xff0c;\u77e9\u9635\u00a0A\u00a0\u7684\u7b2c\u00a0i \u884c\u7b2c\u00a0j \u5217\u7684\u5143\u7d20<img decoding=\"async\" alt=\"a_{ij}\" class=\"mathcode\" src=\"2026-02-27utgrqspr5ft.png\" \/>\u7b49\u4e8e\u77e9\u9635\u00a0B\u00a0\u7684\u7b2c\u00a0i \u884c\u7b2c\u00a0j\u00a0\u5217\u7684\u5143\u7d20\u00a0<img decoding=\"async\" alt=\"b_{ij}\" class=\"mathcode\" src=\"2026-02-275nbno1hyiao.png\" \/>\u3002<\/p>\n<p>\u6362\u53e5\u8bdd\u8bf4&#xff0c;\u4e24\u4e2a\u77e9\u9635\u76f8\u7b49\u610f\u5473\u7740\u5b83\u4eec\u4f5c\u4e3a\u6570\u5b66\u5bf9\u8c61\u662f\u5b8c\u5168\u4e00\u6837\u7684&#xff0c;\u6ca1\u6709\u4efb\u4f55\u533a\u522b\u3002<\/p>\n<h3 id=\"%E7%9F%A9%E9%98%B5%E5%8A%A0%E6%B3%95\">\u77e9\u9635\u52a0\u6cd5<\/h3>\n<p>\u8bbe\u00a0<img decoding=\"async\" alt=\"A&#061;(a_{ij})\" class=\"mathcode\" src=\"2026-02-27tri4facnmeg.png\" \/>\u00a0\u548c\u00a0<img decoding=\"async\" alt=\"B&#061;(a_{ij})\" class=\"mathcode\" src=\"2026-02-275xqb5e2k2cv.png\" \/>\u662f\u4e24\u4e2a\u00a0m\u00d7n \u77e9\u9635&#xff08;\u5373\u884c\u6570\u3001\u5217\u6570\u76f8\u540c&#xff09;\u3002\u5b83\u4eec\u7684\u548c\u00a0A&#043;B\u00a0\u662f\u4e00\u4e2a\u00a0m\u00d7n \u77e9\u9635\u00a0<img decoding=\"async\" alt=\"C&#061;(a_{ij})\" class=\"mathcode\" src=\"2026-02-27wtqcxeqzmpb.png\" \/>&#xff0c;\u5176\u4e2d\u00a0C\u00a0\u7684\u6bcf\u4e2a\u5143\u7d20\u7b49\u4e8e\u00a0A\u00a0\u548c\u00a0B \u5bf9\u5e94\u4f4d\u7f6e\u5143\u7d20\u4e4b\u548c&#xff1a;<\/p>\n<p><img decoding=\"async\" alt=\"c_{ij} &#061; a_{ij} &#043; b_{ij} \\\\quad (1 \\\\leq i \\\\leq m,\\\\ 1 \\\\leq j \\\\leq n).\" class=\"mathcode\" src=\"2026-02-27fmom3il2sgv.png\" \/><\/p>\n<p>\u4f8b\u5982<img decoding=\"async\" alt=\"\\\\mathbf{A} &#061; \\\\begin{bmatrix} 1 &amp; 2 \\\\\\\\ 3 &amp; 4 \\\\end{bmatrix}, \\\\quad \\\\mathbf{B} &#061; \\\\begin{bmatrix} 5 &amp; 6 \\\\\\\\ 7 &amp; 8 \\\\end{bmatrix}.\" class=\"mathcode\" src=\"2026-02-27ja2mprflxna.png\" \/><\/p>\n<p>\u7ed3\u679c\u4e3a&#xff1a;<img decoding=\"async\" alt=\"\\\\mathbf{A} &#043; \\\\mathbf{B} &#061; \\\\begin{bmatrix} 1 &#043; 5 &amp; 2 &#043; 6 \\\\\\\\ 3 &#043; 7 &amp; 4 &#043; 8 \\\\end{bmatrix} &#061; \\\\begin{bmatrix} 6 &amp; 8 \\\\\\\\ 10 &amp; 12 \\\\end{bmatrix}\" class=\"mathcode\" src=\"2026-02-27dpkneurc0ss.png\" \/><\/p>\n<h4 id=\"%E6%B3%A8%E6%84%8F\">\u6ce8\u610f<\/h4>\n<ul>\n<li>\n<p>\u53ea\u6709\u540c\u578b\u77e9\u9635\u624d\u80fd\u76f8\u52a0\u3002\u5982\u679c\u4e24\u4e2a\u77e9\u9635\u7684\u884c\u6570\u6216\u5217\u6570\u4e0d\u540c&#xff0c;\u5219\u5b83\u4eec\u7684\u548c\u6ca1\u6709\u5b9a\u4e49\u3002<\/p>\n<\/li>\n<li>\n<p>\u52a0\u6cd5\u8fd0\u7b97\u53ef\u4ee5\u63a8\u5e7f\u5230\u591a\u4e2a\u77e9\u9635\u76f8\u52a0&#xff0c;\u53ea\u8981\u5b83\u4eec\u90fd\u662f\u540c\u578b\u7684\u3002<\/p>\n<\/li>\n<\/ul>\n<h4 id=\"%E6%80%A7%E8%B4%A8\">\u6027\u8d28<\/h4>\n<li>\n<p>\u4ea4\u6362\u5f8b&#xff1a;A&#043;B&#061;B&#043;A\u3002<\/p>\n<\/li>\n<li>\n<p>\u7ed3\u5408\u5f8b&#xff1a;(A&#043;B)&#043;C&#061;A&#043;(B&#043;C)\u3002<\/p>\n<\/li>\n<li>\n<p>\u5b58\u5728\u96f6\u77e9\u9635&#xff1a;\u5b58\u5728\u4e00\u4e2a\u00a0m\u00d7n \u7684\u96f6\u77e9\u9635\u00a00&#xff08;\u6240\u6709\u5143\u7d20\u4e3a\u96f6&#xff09;&#xff0c;\u4f7f\u5f97\u00a0A&#043;0&#061;A\u3002<\/p>\n<\/li>\n<li>\n<p>\u5b58\u5728\u8d1f\u77e9\u9635&#xff1a;\u5bf9\u4e8e\u6bcf\u4e2a\u77e9\u9635\u00a0A&#xff0c;\u5b58\u5728\u552f\u4e00\u7684\u77e9\u9635\u00a0\u2212A&#xff08;\u79f0\u4e3a\u00a0A\u00a0\u7684\u8d1f\u77e9\u9635&#xff09;&#xff0c;\u5176\u5143\u7d20\u662f\u00a0A\u00a0\u5bf9\u5e94\u5143\u7d20\u7684\u76f8\u53cd\u6570&#xff0c;\u6ee1\u8db3\u00a0A&#043;(\u2212A)&#061;0\u3002<\/p>\n<\/li>\n<h3 id=\"%E7%9F%A9%E9%98%B5%E5%87%8F%E6%B3%95\">\u77e9\u9635\u51cf\u6cd5<\/h3>\n<p>\u5229\u7528\u8d1f\u77e9\u9635&#xff0c;\u53ef\u4ee5\u5b9a\u4e49\u77e9\u9635\u51cf\u6cd5&#xff1a;<img decoding=\"async\" alt=\"\\\\mathbf{A} - \\\\mathbf{B} &#061; \\\\mathbf{A} &#043; (-\\\\mathbf{B})\" class=\"mathcode\" src=\"2026-02-27hp3nfb1puuq.png\" \/><\/p>\n<h3 id=\"%E7%9F%A9%E9%98%B5%E4%B9%98%E6%B3%95\">\u77e9\u9635\u4e58\u6cd5<\/h3>\n<p>\u77e9\u9635\u4e58\u6cd5\u662f\u7ebf\u6027\u4ee3\u6570\u4e2d\u6700\u6838\u5fc3\u7684\u64cd\u4f5c\u4e4b\u4e00&#xff0c;\u4f46\u5b83\u7684\u8ba1\u7b97\u89c4\u5219\u548c\u610f\u4e49\u53ef\u80fd\u4e0e\u5927\u5bb6\u719f\u6089\u7684\u6570\u7684\u4e58\u6cd5\u6709\u5f88\u5927\u4e0d\u540c\u3002\u77e9\u9635\u4e58\u6cd5\u5e76\u4e0d\u662f\u4e24\u4e2a\u540c\u7ef4\u6570\u7684\u77e9\u9635\u5bf9\u5e94\u5143\u7d20\u76f8\u4e58\u3002\u6211\u4eec\u901a\u5e38\u8bf4\u7684\u77e9\u9635\u4e58\u6cd5\u662f\u6307\u4e00\u822c\u77e9\u9635\u4e58\u79ef&#xff08;\u4e5f\u79f0\u4e3a\u70b9\u79ef\u6216\u5185\u79ef\u76f8\u4e58&#xff09;\u3002<\/p>\n<h4 id=\"%E5%8F%AF%E4%B9%98%E6%80%A7\">\u53ef\u4e58\u6027<\/h4>\n<ul>\n<li>\n<p>\u5e76\u4e0d\u662f\u4efb\u610f\u4e24\u4e2a\u77e9\u9635\u90fd\u80fd\u76f8\u4e58\u3002<\/p>\n<\/li>\n<li>\n<p>\u8bbe\u77e9\u9635\u00a0A\u00a0\u7684\u5c3a\u5bf8\u4e3a\u00a0m\u00d7n&#xff08;m\u00a0\u884c\u00a0n\u00a0\u5217&#xff09;&#xff0c;\u77e9\u9635\u00a0B \u7684\u5c3a\u5bf8\u4e3a\u00a0p\u00d7q\u3002\u53ea\u6709\u5f53\u00a0A\u00a0\u7684\u5217\u6570\u7b49\u4e8e\u00a0B \u7684\u884c\u6570\u65f6&#xff0c;\u5373\u00a0n&#061;p&#xff0c;A \u548c\u00a0B \u624d\u80fd\u76f8\u4e58\u3002<\/p>\n<\/li>\n<\/ul>\n<h4 id=\"%E8%AE%A1%E7%AE%97%E8%A7%84%E5%88%99%EF%BC%9A%E2%80%9C%E5%B7%A6%E8%A1%8C%E4%B9%98%E5%8F%B3%E5%88%97%E2%80%9D\">\u8ba1\u7b97\u89c4\u5219&#xff1a;\u201c\u5de6\u884c\u4e58\u53f3\u5217\u201d<\/h4>\n<p>\u5047\u8bbe\u6211\u4eec\u8ba1\u7b97\u00a0C&#061;A\u00d7B&#xff0c;\u7ed3\u679c\u77e9\u9635\u00a0C \u7684\u5c3a\u5bf8\u662f\u00a0m\u00d7q&#xff08;A\u00a0\u7684\u884c\u6570&#xff0c;B\u00a0\u7684\u5217\u6570&#xff09;\u3002\u5982\u4f55\u6c42\u00a0C\u4e2d\u7b2c\u00a0i\u00a0\u884c\u7b2c\u00a0j \u5217\u7684\u5143\u7d20<img decoding=\"async\" alt=\"c_{ij}\" class=\"mathcode\" src=\"2026-02-27s0qc3vcvq1b.png\" \/>\u3002\u4f8b\u5982\u6211\u6709\u4e24\u4e2a\u77e9\u9635A\u548cB\u76f8\u4e58&#xff0c;\u90a3\u4e48\u7ed3\u679c\u5982\u4e0b&#xff1a;<\/p>\n<p><img decoding=\"async\" alt=\"A_{m\\\\times s}B_{s\\\\times n} &#061; C_{m\\\\times n}\" class=\"mathcode\" src=\"2026-02-27ah2npouvxjm.png\" \/><\/p>\n<p>\u53d6\u00a0A \u7684\u7b2c\u00a0i \u884c\u7684\u6bcf\u4e00\u4e2a\u5143\u7d20&#xff0c;\u53d6\u00a0B\u00a0\u7684\u7b2c\u00a0j \u5217\u7684\u6bcf\u4e00\u4e2a\u5143\u7d20&#xff0c;\u5c06\u5b83\u4eec\u5bf9\u5e94\u76f8\u4e58&#xff0c;\u7136\u540e\u6c42\u548c\u3002\u5982\u679c\u6362\u6210\u516c\u5f0f\u5c31\u662f&#xff1a;<img decoding=\"async\" alt=\"$c_{ij} &#061; a_{i1}b_{1j} &#043; a_{i2}b_{2j} &#043; \\\\dots &#043; a_{is}b_{sj} &#061; \\\\sum_{k&#061;1}^s a_{ik}b_{kj}$\" class=\"mathcode\" src=\"2026-02-27gb4hvsf5mnk.png\" \/>&#xff0c;\u5176\u4e2d\u00a0n\u00a0\u662f\u00a0A \u7684\u5217\u6570&#xff08;\u4e5f\u662f\u00a0B\u00a0\u7684\u884c\u6570&#xff09; \u3002<\/p>\n<p>\u8bbe\u77e9\u9635\u00a0A \u548c\u00a0B\u00a0\u5982\u4e0b&#xff1a;<img decoding=\"async\" alt=\"A &#061; \\\\begin{bmatrix} 1 &amp; 2 \\\\\\\\ 3 &amp; 4 \\\\end{bmatrix}, \\\\quad B &#061; \\\\begin{bmatrix} 5 &amp; 6 \\\\\\\\ 7 &amp; 8 \\\\end{bmatrix}\" class=\"mathcode\" src=\"2026-02-27cvgnfejs1fw.png\" \/><\/p>\n<p>\u8ba1\u7b97\u00a0C&#061;A\u00d7B&#xff1a;<\/p>\n<ul>\n<li>\n<p>\u7b2c\u4e00\u884c\u7b2c\u4e00\u5217&#xff1a;<img decoding=\"async\" alt=\"C_{11}\" class=\"mathcode\" src=\"2026-02-27duxm1pahxi4.png\" \/>&#061;1\u00d75&#043;2\u00d77&#061;5&#043;14&#061;19<\/p>\n<\/li>\n<li>\n<p>\u7b2c\u4e00\u884c\u7b2c\u4e8c\u5217&#xff1a;<img decoding=\"async\" alt=\"C_{12}\" class=\"mathcode\" src=\"2026-02-27midrp3yxg30.png\" \/>&#061;1\u00d76&#043;2\u00d78&#061;6&#043;16&#061;22<\/p>\n<\/li>\n<li>\n<p>\u7b2c\u4e8c\u884c\u7b2c\u4e00\u5217&#xff1a;<img decoding=\"async\" alt=\"C_{21}\" class=\"mathcode\" src=\"2026-02-273b0xmsnaqkm.png\" \/>&#061;3\u00d75&#043;4\u00d77&#061;15&#043;28&#061;43<\/p>\n<\/li>\n<li>\n<p>\u7b2c\u4e8c\u884c\u7b2c\u4e8c\u5217&#xff1a;<img decoding=\"async\" alt=\"C_{22}\" class=\"mathcode\" src=\"2026-02-27gwmjrnf4r3g.png\" \/>&#061;3\u00d76&#043;4\u00d78&#061;18&#043;32&#061;50<\/p>\n<\/li>\n<\/ul>\n<p>\u7ed3\u679c\u4e3a&#xff1a;<img decoding=\"async\" alt=\"C &#061; \\\\begin{bmatrix} 19 &amp; 22 \\\\\\\\ 43 &amp; 50 \\\\end{bmatrix}\" class=\"mathcode\" src=\"2026-02-27eeiultktky2.png\" \/><\/p>\n<h4 id=\"%C2%A0%E9%87%8D%E8%A6%81%E6%80%A7%E8%B4%A8%EF%BC%88%E4%B8%8E%E6%95%B0%E7%9A%84%E4%B9%98%E6%B3%95%E4%B8%8D%E5%90%8C%EF%BC%89\">\u00a0\u91cd\u8981\u6027\u8d28&#xff08;\u4e0e\u6570\u7684\u4e58\u6cd5\u4e0d\u540c&#xff09;<\/h4>\n<p>\u77e9\u9635\u4e58\u6cd5\u6709\u5f88\u591a\u8fdd\u53cd\u76f4\u89c9\u7684\u6027\u8d28&#xff0c;\u8fd9\u662f\u521d\u5b66\u8005\u5bb9\u6613\u51fa\u9519\u7684\u5730\u65b9\u3002<\/p>\n<ul>\n<li>\n<p>\u4e0d\u6ee1\u8db3\u4ea4\u6362\u5f8b&#xff1a;\u901a\u5e38\u00a0A\u00d7B &#061; B\u00d7A\u3002\u6709\u65f6\u00a0AXB \u6709\u610f\u4e49&#xff0c;\u4f46\u00a0BXA\u53ef\u80fd\u6839\u672c\u4e0d\u80fd\u4e58&#xff08;\u56e0\u4e3a\u7ef4\u5ea6\u5bf9\u4e0d\u4e0a&#xff09;\u3002\u5373\u4f7f\u90fd\u80fd\u4e58&#xff0c;\u7ed3\u679c\u4e5f\u5f80\u5f80\u4e0d\u540c\u3002\u5982\u4e0b\u6240\u793a<\/p>\n<ul>\n<li>\n<p><img loading=\"lazy\" decoding=\"async\" alt=\"\" height=\"229\" src=\"2026-02-27z53brk0o5xh.png\" width=\"524\" \/><\/p>\n<\/li>\n<\/ul>\n<\/li>\n<li>\n<p>\u4e0d\u6ee1\u8db3\u6570\u4e58\u6cd5\u5b9a\u5f8b&#xff1a;\u4f8b\u5982 AB&#061;AC&#xff0c;\u4f46\u662fB\u548cC\u4e0d\u4e00\u5b9a\u76f8\u7b49\u3002\u5982\u4e0b\u6240\u793a<\/p>\n<ul>\n<li>\n<p><img loading=\"lazy\" decoding=\"async\" alt=\"\" height=\"217\" src=\"2026-02-27g4t5z2earpy.png\" width=\"529\" \/><\/p>\n<\/li>\n<\/ul>\n<\/li>\n<li>\u6ee1\u8db3\u7ed3\u5408\u5f8b&#xff1a;(AB)C&#061;A(BC)&#xff0c;\u524d\u63d0\u662f\u7ef4\u5ea6\u5141\u8bb8\u3002<\/li>\n<li>\n<p>\u6ee1\u8db3\u5206\u914d\u5f8b&#xff1a;A(B&#043;C)&#061;AB&#043;AC\u3002<\/p>\n<\/li>\n<li>\n<p>\u96f6\u56e0\u5b50\u5b58\u5728&#xff1a;\u4e24\u4e2a\u975e\u96f6\u77e9\u9635\u76f8\u4e58&#xff0c;\u7ed3\u679c\u53ef\u80fd\u662f\u96f6\u77e9\u9635&#xff0c;\u5982\u4e0b\u6240\u793a<\/p>\n<p> <img decoding=\"async\" alt=\"\\\\begin{bmatrix} 1 &amp; 1 \\\\\\\\ 1 &amp; 1 \\\\end{bmatrix} \\\\times \\\\begin{bmatrix} 1 &amp; 1 \\\\\\\\ -1 &amp; -1 \\\\end{bmatrix} &#061; \\\\begin{bmatrix} 0 &amp; 0 \\\\\\\\ 0 &amp; 0 \\\\end{bmatrix}\" class=\"mathcode\" src=\"2026-02-27os5x0hqsyu4.png\" \/><\/li>\n<\/ul>\n<h2 id=\"%E6%96%B9%E9%98%B5%E7%9A%84%E5%B9%82\">\u65b9\u9635\u7684\u5e42<\/h2>\n<p>\u53ea\u6709\u65b9\u9635\u624d\u80fd\u7b97\u5e42&#xff0c;\u8bbe A \u662f n \u9636\u65b9\u9635&#xff0c;k \u662f\u6b63\u6574\u6570\u5219\u6709<img decoding=\"async\" alt=\"A^k &#061; \\\\underbrace{A\\\\cdot A\\\\cdot \\\\dots \\\\cdot A}_{k\\\\text{}}\" class=\"mathcode\" src=\"2026-02-27v31ar2ktrv4.png\" \/><\/p>\n<h3 id=\"%E5%AE%9A%E5%BE%8B\">\u5b9a\u5f8b<\/h3>\n<p><img decoding=\"async\" alt=\"A^k A^l &#061; A^{k&#043;l},\\\\quad (A^k)^l &#061; A^{kl}\" class=\"mathcode\" src=\"2026-02-27frlv52znz41.png\" \/><\/p>\n<\/p>\n<p>\u4e00\u822c\u6765\u8bf4\u00a0\u00a0<img decoding=\"async\" alt=\"$(AB)^k \\\\neq A^k B^k$\" class=\"mathcode\" src=\"2026-02-27wzfvg44mkqn.png\" \/>&#xff0c;\u56e0\u4e3a\u77e9\u9635\u4e58\u6cd5\u4e0d\u6ee1\u8db3\u4ea4\u6362\u5f8b\u3002\u4f46\u5982\u679c\u00a0AB&#061;BA&#xff0c;\u7b49\u5f0f\u6210\u7acb\u3002<\/p>\n<p>\u8f6c\u7f6e&#xff1a;<img decoding=\"async\" alt=\"$(A^k)^T &#061; (A^T)^k$\" class=\"mathcode\" src=\"2026-02-273pp3n1e520w.png\" \/><\/p>\n<h2 id=\"%E8%BD%AC%E7%BD%AE%E7%9F%A9%E9%98%B5\">\u8f6c\u7f6e\u77e9\u9635<\/h2>\n<p>\u5c06\u4e00\u4e2a\u00a0m\u00d7n \u7684\u77e9\u9635\u00a0A \u7684\u884c\u548c\u5217\u4e92\u6362&#xff0c;\u5f97\u5230\u7684\u00a0n\u00d7m \u7684\u65b0\u77e9\u9635\u79f0\u4e3a\u00a0A\u00a0\u7684\u8f6c\u7f6e\u77e9\u9635&#xff0c;\u8bb0\u4f5c\u00a0<img decoding=\"async\" alt=\"A^T\" class=\"mathcode\" src=\"2026-02-27h3v1gl2zcpi.png\" \/>&#xff08;\u6216\u00a0A\u2032&#xff09;\u3002<\/p>\n<p>\u5143\u7d20\u5173\u7cfb&#xff1a;\u5982\u679c\u00a0<img decoding=\"async\" alt=\"B &#061; A^T\" class=\"mathcode\" src=\"2026-02-27mqluo14mzkr.png\" \/>&#xff0c;\u90a3\u4e48\u00a0B\u00a0\u4e2d\u7b2c\u00a0i 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\/><\/p>\n<p>\u4e58\u79ef\u7684\u8f6c\u7f6e&#xff08;\u53cd\u8f6c\u987a\u5e8f&#xff09;&#xff1a;<img decoding=\"async\" alt=\"(AB)^T &#061; B^T A^T\" class=\"mathcode\" src=\"2026-02-271q0cs25055q.png\" \/><\/p>\n<p>\u00a0 \u00a0 \u00a0 \u00a0 \u63a8\u5bfc\u4e00\u4e0b<img decoding=\"async\" alt=\"(AB)^T &#061; B^T A^T\" class=\"mathcode\" src=\"2026-02-271q0cs25055q.png\" \/>&#xff0c;\u8bbe\u00a0<img decoding=\"async\" alt=\"A &#061; (a_{ij})_{m \\\\times s}\" class=\"mathcode\" src=\"2026-02-27moqal0piirm.png\" \/>&#xff0c;\u6839\u636e\u77e9\u9635\u7684\u53ef\u4e58\u6027\u8d28\u90a3\u4e48<img decoding=\"async\" alt=\"B &#061; (b_{ij})_{s \\\\times n}\" class=\"mathcode\" src=\"2026-02-27wpduzijd3pf.png\" \/>&#xff0c;\u6240\u4ee5\u77e9\u9635A\u548cB\u7684\u8f6c\u7f6e\u77e9\u9635\u4e3a&#xff1a;<img decoding=\"async\" alt=\"A^T &#061; (a_{ji})_{s \\\\times m} \\\\quad B^T &#061; (b_{ji})_{n \\\\times s}\" class=\"mathcode\" src=\"2026-02-27ksoqrtuyxdi.png\" \/>&#xff0c;\u90a3\u4e48\u5c31\u6709<img 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