{"id":1605,"date":"2024-12-01T19:20:06","date_gmt":"2024-12-01T11:20:06","guid":{"rendered":"https:\/\/thereisno.top\/?p=1605"},"modified":"2024-12-07T21:21:24","modified_gmt":"2024-12-07T13:21:24","slug":"%e7%9f%a9%e9%98%b5%e5%af%b9%e8%a7%92%e5%8c%96","status":"publish","type":"post","link":"https:\/\/thereisno.top\/?p=1605","title":{"rendered":"\u77e9\u9635\u5bf9\u89d2\u5316"},"content":{"rendered":"\n

\u4e00\u3001\u4ec0\u4e48\u6837\u7684n\u9636\u77e9\u9635\u624d\u80fd\u5bf9\u89d2\u5316\uff1f<\/h2>\n

\u5148\u8bf4\u7ed3\u8bba \n{<\/mo>a<\/mi>.<\/mo><\/mtd><\/mi>\u7279\u5f81\u503c\u65e0\u91cd\u6839<\/mo>\u2705<\/mo><\/mrow><\/mtd><\/mtr>b<\/mi>.<\/mo><\/mtd><\/mi>\u6709\u91cd\u6839<\/mo>{<\/mo>b<\/mi>.1<\/mn>.<\/mo><\/mtd><\/mi>\u5384\u7c73\u7279\u77e9\u9635<\/mo>(<\/mo>H<\/mi>e<\/mi>r<\/mi>m<\/mi>i<\/mi>t<\/mi>i<\/mi>a<\/mi>n<\/mi>)<\/mo>,<\/mo><\/mtd><\/mtr><\/mtd><\/mi>\u7279\u522b\u7684\u5bf9\u79f0\u5b9e\u6570\u77e9\u9635<\/mo>\u2705<\/mo><\/mrow><\/mtd><\/mtr>b<\/mi>.2<\/mn>.<\/mo><\/mtd><\/mi>\u975e\u5384\u77e9\u9635<\/mo>{<\/mo>b<\/mi>.2<\/mn>.<\/mo><\/mtd>1.<\/mn>\u51e0\u4f55\u91cd\u6570<\/mo><\/mtd><\/mtr><\/mtd><\/mi>=\u4ee3\u6570\u91cd\u6570<\/mo>\u2705<\/mo><\/mrow><\/mtd><\/mtr>b<\/mi>.2<\/mn>.<\/mo><\/mtd>2.<\/mn>\u51e0\u4f55\u91cd\u6570<\/mo><\/mtd><\/mtr><\/mtd><\/mi>\u2260\u4ee3\u6570\u91cd\u6570<\/mo>\u274c<\/mo><\/mrow><\/mtd><\/mtr><\/mtable><\/mo><\/mrow><\/mtd><\/mtr><\/mtable><\/mo><\/mrow><\/mtd><\/mtr><\/mtable><\/mo><\/mrow><\/math>\n<\/p>\n

\u5b9a\u74061\uff1a<\/h3>\n

\u8bbe \u03bb<\/mi>1<\/mn><\/msub>,<\/mo>\u03bb<\/mi>2<\/mn><\/msub>,<\/mo>\u2026<\/mi>,<\/mo>\u03bb<\/mi>m<\/mi><\/msub><\/mrow>\\lambda_1,\\lambda_2,\\dots,\\lambda_m<\/annotation><\/semantics><\/math> \u662f\u65b9\u9635A<\/mi>A<\/annotation><\/semantics><\/math>\u7684m\u4e2a\u7279\u5f81\u503c\uff0cp<\/mi>1<\/mn><\/msub>,<\/mo>p<\/mi>2<\/mn><\/msub>,<\/mo>\u2026<\/mi>,<\/mo>p<\/mi>m<\/mi><\/msub><\/mrow>p_1,p_2,\\dots,p_m<\/annotation><\/semantics><\/math>\u4f9d\u6b21\u662f\u4e0e\u4e4b\u5bf9\u5e94\u7684\u7279\u5f81\u5411\u91cf\uff0c\u5982\u679c\u03bb<\/mi>1<\/mn><\/msub>,<\/mo>\u03bb<\/mi>2<\/mn><\/msub>,<\/mo>\u2026<\/mi>,<\/mo>\u03bb<\/mi>m<\/mi><\/msub><\/mrow>\\lambda_1,\\lambda_2,\\dots,\\lambda_m<\/annotation><\/semantics><\/math>\u5404\u4e0d\u76f8\u7b49\uff0c\u5219p<\/mi>1<\/mn><\/msub>,<\/mo>p<\/mi>2<\/mn><\/msub>,<\/mo>\u2026<\/mi>,<\/mo>p<\/mi>m<\/mi><\/msub><\/mrow>p_1,p_2,\\dots,p_m<\/annotation><\/semantics><\/math>\u7ebf\u6027\u65e0\u5173\u3002<\/p>\n\n\n\n\n\n\n\n

\u5b9a\u74062\uff1a<\/h3>\n

n\u9636\u77e9\u9635A<\/mi>A<\/annotation><\/semantics><\/math>\u4e0e\u5bf9\u89d2\u77e9\u9635\u76f8\u4f3c\uff08\u5373A<\/mi>A<\/annotation><\/semantics><\/math>\u80fd\u5bf9\u89d2\u5316\uff09\u7684\u5145\u5206\u5fc5\u8981\u6761\u4ef6\u662fA<\/mi>A<\/annotation><\/semantics><\/math>\u6709n<\/mi>n<\/annotation><\/semantics><\/math>\u4e2a\u7ebf\u6027\u65e0\u5173\u7684\u7279\u5f81\u5411\u91cf\u3002<\/p>\n

\u63a8\u8bba\uff1a<\/h3>\n

\u5982\u679cn\u9636\u77e9\u9635A<\/mi>A<\/annotation><\/semantics><\/math>\u7684n<\/mi>n<\/annotation><\/semantics><\/math>\u4e2a\u7279\u5f81\u503c\u4e92\u4e0d\u76f8\u7b49\uff0c\u5219A<\/mi>A<\/annotation><\/semantics><\/math>\u4e0e\u5bf9\u89d2\u77e9\u9635\u76f8\u4f3c\u3002<\/p>\n

\u4e8c\u3001\u6839\u636e\u4ee5\u4e0a\u5b9a\u7406\u548c\u63a8\u7406\u7279\u5f81\u503c\u65e0\u91cd\u6839\u7684a\u548cb.2.1\u60c5\u51b5\u4e00\u5b9a\u53ef\u4ee5\u5bf9\u89d2\u5316\u3002<\/h2>\n

\u4e09\u3001\u6709\u91cd\u6839\u60c5\u51b5b.1\u60c5\u51b5<\/h2>\n

3.1 \u5384\u7c73\u7279\u77e9\u9635<\/h4>\n

\u5384\u7c73\u7279\u77e9\u9635\u662f\u6ee1\u8db3A<\/mi>H<\/mi><\/msup>=<\/mo>A<\/mi><\/mrow>A^H=A<\/annotation><\/semantics><\/math>\u7684\u77e9\u9635\uff0c\u5373A<\/mi>H<\/mi><\/msup>A^H<\/annotation><\/semantics><\/math>\u662fA<\/mi>A<\/annotation><\/semantics><\/math>\u7684\u5171\u8f6d\u8f6c\u7f6e\u77e9\u9635\u3002<\/p>\n

3.2 \u9149\u77e9\u9635<\/h4>\n

\u6ee1\u8db3A<\/mi>H<\/mi><\/msup>A<\/mi>=<\/mo>I<\/mi><\/mrow>A^HA=I<\/annotation><\/semantics><\/math>\u7684\u77e9\u9635\u3002\u9149\u77e9\u9635\uff0c\u5176\u5217\u5411\u91cf\u662f\u89c4\u8303\u6b63\u4ea4\u7684\uff0c\u5176\u79e9\u5fc5\u4e3an\u3002 A<\/mi>\u2212<\/mo>1<\/mn><\/mrow><\/msup>=<\/mo>A<\/mi>H<\/mi><\/msup><\/mrow>A^{-1}=A^H<\/annotation><\/semantics><\/math> n\u9636n\u7ef4\u7ebf\u6027\u65e0\u5173\u5411\u91cf\u5fc5\u53ef\u4ee5\u901a\u8fc7\u65bd\u5bc6\u7279\u6b63\u4ea4\u5316\u5f97\u5230\u6807\u51c6\u6b63\u4ea4\u57fa\u77e9\u9635\uff0c\u5373\u662f\u9149\u77e9\u9635\u3002<\/p>\n\n

3.3 \u8212\u5c14\u5316\u77e9\u9635<\/h4>\n

\u8bben\u9636\u77e9\u9635A<\/mi>A<\/annotation><\/semantics><\/math>\u7684\u7279\u5f81\u503c\u03bb<\/mi>k<\/mi><\/msub>\\lambda_k<\/annotation><\/semantics><\/math>\u6709k<\/mi>k<\/annotation><\/semantics><\/math>\u91cd\u6839\uff0c\u5bf9\u5e94m<\/mi>m<\/annotation><\/semantics><\/math>\u4e2a\u7279\u5f81\u503c\uff0cp<\/mi>1<\/mn><\/msub>,<\/mo>p<\/mi>2<\/mn><\/msub>,<\/mo>\u2026<\/mi>,<\/mo>p<\/mi>m<\/mi><\/msub><\/mrow>p_1,p_2,\\dots,p_m<\/annotation><\/semantics><\/math>\u4f9d\u6b21\u662f\u4e0e\u4e4b\u5bf9\u5e94\u7684\u7279\u5f81\u5411\u91cf,\u7ec4\u6210\u4e00\u7ec4\u57fa\uff0c\u628a{<\/mo>p<\/mi>1<\/mn><\/msub>,<\/mo>p<\/mi>2<\/mn><\/msub>,<\/mo>\u2026<\/mi>,<\/mo>p<\/mi>m<\/mi><\/msub>}<\/mo><\/mrow>\\{p_1,p_2,\\dots,p_m\\}<\/annotation><\/semantics><\/math>\u6269\u5145\u81f3n\u4e2a\uff08n\u7ef4\u7684\u6700\u5927\u7ebf\u6027\u65e0\u5173\u7ec4\u662fn\u4e2a\uff09\uff0c\u5e76\u65bd\u5bc6\u7279\u6b63\u4ea4\u5316\uff0c\u5f97\u5230P<\/mi>=<\/mo>(<\/mo>p<\/mi>1<\/mn><\/msub>,<\/mo>p<\/mi>2<\/mn><\/msub>,<\/mo>\u2026<\/mi>,<\/mo>p<\/mi>m<\/mi><\/msub>,<\/mo>p<\/mi>m<\/mi>+<\/mo>1<\/mn><\/mrow><\/msub>,<\/mo>\u2026<\/mi>,<\/mo>p<\/mi>n<\/mi><\/msub>)<\/mo><\/mrow><\/mrow>P=(p_1,p_2,\\dots,p_m,p_{m+1},\\dots,p_n)<\/annotation><\/semantics><\/math> A<\/mi>P<\/mi>=<\/mo>(<\/mo>\u03bb<\/mi>k<\/mi><\/msub>p<\/mi>1<\/mn><\/msub>,<\/mo>\u03bb<\/mi>k<\/mi><\/msub>p<\/mi>2<\/mn><\/msub>,<\/mo>\u2026<\/mi>,<\/mo>\u03bb<\/mi>k<\/mi><\/msub>p<\/mi>m<\/mi><\/msub>,<\/mo>A<\/mi>p<\/mi>m<\/mi>+<\/mo>1<\/mn><\/mrow><\/msub>,<\/mo>A<\/mi>p<\/mi>m<\/mi>+<\/mo>2<\/mn><\/mrow><\/msub>,<\/mo>\u2026<\/mi>,<\/mo>A<\/mi>p<\/mi>n<\/mi><\/msub>)<\/mo><\/mrow><\/mrow>AP=(\\lambda_kp_1,\\lambda_kp_2,\\dots,\\lambda_kp_m,Ap_{m+1},Ap_{m+2},\\dots,Ap_n)<\/annotation><\/semantics><\/math><\/p>\n

P<\/mi>H<\/mi><\/msup>A<\/mi>P<\/mi>=<\/mo>(<\/mo>p<\/mi>1<\/mn>H<\/mi><\/msubsup><\/mtd><\/mtr>p<\/mi>2<\/mn>H<\/mi><\/msubsup><\/mtd><\/mtr>p<\/mi>3<\/mn>H<\/mi><\/msubsup><\/mtd><\/mtr>\u22ee<\/mi><\/mtd><\/mtr>p<\/mi>m<\/mi>H<\/mi><\/msubsup><\/mtd><\/mtr>p<\/mi>m<\/mi>+<\/mo>1<\/mn><\/mrow>H<\/mi><\/msubsup><\/mtd><\/mtr>\u22ee<\/mi><\/mtd><\/mtr>p<\/mi>n<\/mi><\/msub><\/mtd><\/mtr><\/mtable>)<\/mo><\/mrow>(<\/mo>\u03bb<\/mi>k<\/mi><\/msub>p<\/mi>1<\/mn><\/msub>,<\/mo>\u03bb<\/mi>k<\/mi><\/msub>p<\/mi>2<\/mn><\/msub>,<\/mo>\u2026<\/mi>,<\/mo>\u03bb<\/mi>k<\/mi><\/msub>p<\/mi>m<\/mi><\/msub>,<\/mo>A<\/mi>p<\/mi>m<\/mi>+<\/mo>1<\/mn><\/mrow><\/msub>,<\/mo>A<\/mi>p<\/mi>m<\/mi>+<\/mo>2<\/mn><\/mrow><\/msub>,<\/mo>\u2026<\/mi>,<\/mo>A<\/mi>p<\/mi>n<\/mi><\/msub>)<\/mo><\/mrow><\/mrow>\nP^HAP=\n\\begin{pmatrix} \np_1^H \\\\\np_2^H\\\\\np_3^H\\\\\n\\vdots\\\\\np_m^H\\\\\np_{m+1}^H\\\\\n\\vdots\\\\\np_{n}\n\\end{pmatrix}(\\lambda_kp_1,\\lambda_kp_2,\\dots,\\lambda_kp_m,Ap_{m+1},Ap_{m+2},\\dots,Ap_n)\n<\/annotation><\/semantics><\/math><\/p>\n

\u82e5A<\/mi>=<\/mo>(<\/mo>a<\/mi>i<\/mi>j<\/mi><\/mrow><\/msub>)<\/mo><\/mrow>,<\/mo>p<\/mi>j<\/mi><\/msub>=<\/mo>(<\/mo>q<\/mi>i<\/mi>j<\/mi><\/mrow><\/msub>)<\/mo><\/mrow><\/mrow>A=(a_{ij}), p_j=(q_{ij})<\/annotation><\/semantics><\/math> \u56e0\u4e3aP<\/mi>H<\/mi><\/msup>P^H<\/annotation><\/semantics><\/math>\u7684\u6b63\u4ea4\u6027\uff0c\u6240\u4ee5\uff0c<\/p>\n

P<\/mi>H<\/mi><\/msup>A<\/mi>P<\/mi><\/mtd>=<\/mo>(<\/mo>\u03bb<\/mi>k<\/mi><\/msub><\/mtd><\/mtd><\/mtd><\/mtd>p<\/mi>1<\/mn>H<\/mi><\/msubsup>A<\/mi>p<\/mi>m<\/mi>+<\/mo>1<\/mn><\/mrow><\/msub><\/mtd>\u22ef<\/mi><\/mtd>p<\/mi>1<\/mn>H<\/mi><\/msubsup>A<\/mi>p<\/mi>n<\/mi><\/msub><\/mtd><\/mtr><\/mtd>\u03bb<\/mi>k<\/mi><\/msub><\/mtd><\/mtd><\/mtd>p<\/mi>2<\/mn>H<\/mi><\/msubsup>A<\/mi>p<\/mi>m<\/mi>+<\/mo>1<\/mn><\/mrow><\/msub><\/mtd>\u22ef<\/mi><\/mtd>p<\/mi>2<\/mn>H<\/mi><\/msubsup>A<\/mi>p<\/mi>n<\/mi><\/msub><\/mtd><\/mtr><\/mtd><\/mtd>\u22f1<\/mi><\/mtd><\/mtd>\u22ee<\/mi><\/mtd><\/mtd>\u22ee<\/mi><\/mtd><\/mtr><\/mtd><\/mtd><\/mtd>\u03bb<\/mi>k<\/mi><\/msub><\/mtd>p<\/mi>m<\/mi>H<\/mi><\/msubsup>A<\/mi>p<\/mi>m<\/mi>+<\/mo>1<\/mn><\/mrow><\/msub><\/mtd>\u22ef<\/mi><\/mtd>p<\/mi>m<\/mi>H<\/mi><\/msubsup>A<\/mi>p<\/mi>n<\/mi><\/msub><\/mtd><\/mtr>0<\/mn><\/mtd>0<\/mn><\/mtd>\u22ef<\/mi><\/mtd>0<\/mn><\/mtd>p<\/mi>m<\/mi>+<\/mo>1<\/mn><\/mrow>H<\/mi><\/msubsup>A<\/mi>p<\/mi>m<\/mi>+<\/mo>1<\/mn><\/mrow><\/msub><\/mtd>\u22ef<\/mi><\/mtd>p<\/mi>m<\/mi>+<\/mo>1<\/mn><\/mrow>H<\/mi><\/msubsup>A<\/mi>p<\/mi>n<\/mi><\/msub><\/mtd><\/mtr>\u22ee<\/mi><\/mtd>\u22ee<\/mi><\/mtd><\/mtd>\u22ee<\/mi><\/mtd>\u22ee<\/mi><\/mtd><\/mtd>\u22ee<\/mi><\/mtd><\/mtr>0<\/mn><\/mtd>0<\/mn><\/mtd>\u22ef<\/mi><\/mtd>0<\/mn><\/mtd>p<\/mi>n<\/mi>H<\/mi><\/msubsup>A<\/mi>p<\/mi>m<\/mi>+<\/mo>1<\/mn><\/mrow><\/msub><\/mtd>\u22ef<\/mi><\/mtd>p<\/mi>n<\/mi>H<\/mi><\/msubsup>A<\/mi>p<\/mi>n<\/mi><\/msub><\/mtd><\/mtr><\/mtable>)<\/mo><\/mrow><\/mtd><\/mtr><\/mtable>\n\\begin{aligned}\nP^HAP &=\\begin{pmatrix} \\lambda_{k}& & & & p^H_1Ap_{m+1}&\\cdots&p^H_1Ap_{n} \\\\ & \\lambda_{k} & & & p^H_2Ap_{m+1}&\\cdots&p^H_2Ap_{n}\\\\ & & \\ddots & & \\vdots& &\\vdots \\\\ & & & \\lambda_{k} & p^H_mAp_{m+1}&\\cdots&p^H_mAp_{n}\\\\ 0 & 0 & \\cdots & 0 & p^H_{m+1}Ap_{m+1}&\\cdots&p^H_{m+1}Ap_{n} \\\\\\vdots& \\vdots& & \\vdots& \\vdots& &\\vdots \\\\0&0& \\cdots & 0&p^H_nAp_{m+1}&\\cdots&p^H_nAp_{n}\\\\ \\end{pmatrix} \n\\end{aligned}\n<\/annotation><\/semantics><\/math> P\u4e3a\u6211\u4eec\u6784\u9020\u7684\u9149\u77e9\u9635\uff0c\u4e8e\u662f\u21d2<\/mo>\\Rightarrow<\/annotation><\/semantics><\/math>\uff0c P<\/mi>\u2212<\/mo>1<\/mn><\/mrow><\/msup>A<\/mi>P<\/mi><\/mtd>=<\/mo>P<\/mi>H<\/mi><\/msup>A<\/mi>P<\/mi><\/mtd>=<\/mo>(<\/mo>\u03bb<\/mi>k<\/mi><\/msub><\/mtd><\/mtd><\/mtd><\/mtd>p<\/mi>1<\/mn>H<\/mi><\/msubsup>A<\/mi>p<\/mi>m<\/mi>+<\/mo>1<\/mn><\/mrow><\/msub><\/mtd>\u22ef<\/mi><\/mtd>p<\/mi>1<\/mn>H<\/mi><\/msubsup>A<\/mi>p<\/mi>n<\/mi><\/msub><\/mtd><\/mtr><\/mtd>\u03bb<\/mi>k<\/mi><\/msub><\/mtd><\/mtd><\/mtd>p<\/mi>2<\/mn>H<\/mi><\/msubsup>A<\/mi>p<\/mi>m<\/mi>+<\/mo>1<\/mn><\/mrow><\/msub><\/mtd>\u22ef<\/mi><\/mtd>p<\/mi>2<\/mn>H<\/mi><\/msubsup>A<\/mi>p<\/mi>n<\/mi><\/msub><\/mtd><\/mtr><\/mtd><\/mtd>\u22f1<\/mi><\/mtd><\/mtd>\u22ee<\/mi><\/mtd><\/mtd>\u22ee<\/mi><\/mtd><\/mtr><\/mtd><\/mtd><\/mtd>\u03bb<\/mi>k<\/mi><\/msub><\/mtd>p<\/mi>m<\/mi>H<\/mi><\/msubsup>A<\/mi>p<\/mi>m<\/mi>+<\/mo>1<\/mn><\/mrow><\/msub><\/mtd>\u22ef<\/mi><\/mtd>p<\/mi>m<\/mi>H<\/mi><\/msubsup>A<\/mi>p<\/mi>n<\/mi><\/msub><\/mtd><\/mtr>0<\/mn><\/mtd>0<\/mn><\/mtd>\u22ef<\/mi><\/mtd>0<\/mn><\/mtd>p<\/mi>m<\/mi>+<\/mo>1<\/mn><\/mrow>H<\/mi><\/msubsup>A<\/mi>p<\/mi>m<\/mi>+<\/mo>1<\/mn><\/mrow><\/msub><\/mtd>\u22ef<\/mi><\/mtd>p<\/mi>m<\/mi>+<\/mo>1<\/mn><\/mrow>H<\/mi><\/msubsup>A<\/mi>p<\/mi>n<\/mi><\/msub><\/mtd><\/mtr>\u22ee<\/mi><\/mtd>\u22ee<\/mi><\/mtd><\/mtd>\u22ee<\/mi><\/mtd>\u22ee<\/mi><\/mtd><\/mtd>\u22ee<\/mi><\/mtd><\/mtr>0<\/mn><\/mtd>0<\/mn><\/mtd>\u22ef<\/mi><\/mtd>0<\/mn><\/mtd>p<\/mi>n<\/mi>H<\/mi><\/msubsup>A<\/mi>p<\/mi>m<\/mi>+<\/mo>1<\/mn><\/mrow><\/msub><\/mtd>\u22ef<\/mi><\/mtd>p<\/mi>n<\/mi>H<\/mi><\/msubsup>A<\/mi>p<\/mi>n<\/mi><\/msub><\/mtd><\/mtr><\/mtable>)<\/mo><\/mrow><\/mtd><\/mtr><\/mtd>=<\/mo>B<\/mi><\/mtd><\/mtr><\/mtable>\n\\begin{equation}\n\\begin{aligned}\nP^{-1}AP&=P^HAP\n&=\\begin{pmatrix} \\lambda_{k}& & & & p^H_1Ap_{m+1}&\\cdots&p^H_1Ap_{n} \\\\ & \\lambda_{k} & & & p^H_2Ap_{m+1}&\\cdots&p^H_2Ap_{n}\\\\ & & \\ddots & & \\vdots& &\\vdots \\\\ & & & \\lambda_{k} & p^H_mAp_{m+1}&\\cdots&p^H_mAp_{n}\\\\ 0 & 0 & \\cdots & 0 & p^H_{m+1}Ap_{m+1}&\\cdots&p^H_{m+1}Ap_{n} \\\\\\vdots& \\vdots& & \\vdots& \\vdots& &\\vdots \\\\0&0& \\cdots & 0&p^H_nAp_{m+1}&\\cdots&p^H_nAp_{n}\\\\ \\end{pmatrix} \n\\\\\n&=B\n\\end{aligned}\n\\end{equation}\n<\/annotation><\/semantics><\/math> \u4e3a\u4e66\u5199\u65b9\u4fbf\uff0c\u5c06(1)\u5f0fB<\/mi>B<\/annotation><\/semantics><\/math>\u7b80\u5199\u4e3a\u5757\u77e9\u9635:<\/p>\n\n\nB<\/mi><\/mtd><\/mi>=<\/mo>(<\/mo>\u03bb<\/mi>k<\/mi><\/mrow><\/msub><\/mtd><\/mtd><\/mtd><\/mtd>\u2217<\/mo><\/mtd>\u22ef<\/mo><\/mtd>\u2217<\/mo><\/mtd><\/mtr><\/mtd>\u03bb<\/mi>k<\/mi><\/mrow><\/msub><\/mtd><\/mtd><\/mtd>\u2217<\/mo><\/mtd>\u22ef<\/mo><\/mtd>\u2217<\/mo><\/mtd><\/mtr><\/mtd><\/mtd>\u22f1<\/mo><\/mtd><\/mtd>\u22ee<\/mo><\/mrow><\/mtd><\/mtd>\u22ee<\/mo><\/mrow><\/mtd><\/mtr><\/mtd><\/mtd><\/mtd>\u03bb<\/mi>k<\/mi><\/mrow><\/msub><\/mtd>\u2217<\/mo><\/mtd>\u22ef<\/mo><\/mtd>\u2217<\/mo><\/mtd><\/mtr>0<\/mn><\/mtd>0<\/mn><\/mtd>\u22ef<\/mo><\/mtd>0<\/mn><\/mtd>\u2217<\/mo><\/mtd>\u22ef<\/mo><\/mtd>\u2217<\/mo><\/mtd><\/mtr>\u22ee<\/mo><\/mrow><\/mtd>\u22ee<\/mo><\/mrow><\/mtd><\/mtd>\u22ee<\/mo><\/mrow><\/mtd>\u22ee<\/mo><\/mrow><\/mtd><\/mtd>\u22ee<\/mo><\/mrow><\/mtd><\/mtr>0<\/mn><\/mtd>0<\/mn><\/mtd>\u22ef<\/mo><\/mtd>0<\/mn><\/mtd>\u2217<\/mo><\/mtd>\u22ef<\/mo><\/mtd>\u2217<\/mo><\/mtd><\/mtr><\/mtable>)<\/mo><\/mrow><\/mtd><\/mtr><\/mtd><\/mi>=<\/mo>(<\/mo><\/mtd><\/mtr>\u03bb<\/mi>k<\/mi><\/mrow><\/msub><\/mtd><\/mtd><\/mtr><\/mtd>\u22f1<\/mo><\/mtd><\/mtd>W<\/mi><\/mtd><\/mtr><\/mtd><\/mtd>\u03bb<\/mi>k<\/mi><\/mrow><\/msub><\/mtd><\/mtd><\/mtr><\/mtd>O<\/mi><\/mtd><\/mtd>M<\/mi><\/mtd><\/mtr><\/mtable>)<\/mo><\/mrow><\/mtd><\/mtr><\/mtable><\/math>\n

\u5176\u4e2dM<\/mi>M<\/annotation><\/semantics><\/math>\u77e9\u9635\u53ef\u4ee5\u91cd\u590d\u4e0a\u9762\u7684\u6b65\u9aa4\uff0c\u6700\u7ec8\u5f97\u5230\u4e0a\u4e09\u89d2\u77e9\u9635\u3002<\/p>\n

A<\/mi>A<\/annotation><\/semantics><\/math>\u4e0eB<\/mi>B<\/annotation><\/semantics><\/math>\u76f8\u4f3c\uff0c\u6839\u636e\u6709\u5173\u5b9a\u7406\uff0c\u5b83\u4eec\u5177\u6709\u76f8\u540c\u7684\u7279\u5f81\u503c\u3002 |<\/mo>A<\/mi>\u2212<\/mo>\u03bb<\/mi>E<\/mi>|<\/mo><\/mrow>=<\/mo>|<\/mo>B<\/mi>\u2212<\/mo>\u03bb<\/mi>E<\/mi>|<\/mo><\/mrow><\/mrow>|A-\\lambda E|=|B-\\lambda E|<\/annotation><\/semantics><\/math><\/p>\n\n|<\/mo>B<\/mi>\u2212<\/mo>\u03bb<\/mi>E<\/mi>|<\/mo><\/mtd><\/mi>=<\/mo>(<\/mo>\u03bb<\/mi>k<\/mi><\/mrow><\/msub>\u2212<\/mo>\u03bb<\/mi><\/mtd><\/mtd><\/mtr><\/mtd>\u22f1<\/mo><\/mtd><\/mtd>W<\/mi><\/mtd><\/mtr><\/mtd><\/mtd>\u03bb<\/mi>k<\/mi><\/mrow><\/msub>\u2212<\/mo>\u03bb<\/mi><\/mtd><\/mtd><\/mtr><\/mtd>O<\/mi><\/mtd><\/mtd>M<\/mi>\u2212<\/mo>\u03bb<\/mi>E<\/mi><\/mtd><\/mtr><\/mtable>)<\/mo><\/mrow><\/mtd><\/mtr><\/mtd><\/mi>=<\/mo>(<\/mo>\u03bb<\/mi>k<\/mi><\/mrow><\/msub>\u2212<\/mo>\u03bb<\/mi>)<\/mo>m<\/mi><\/msup>g<\/mi>(<\/mo>\u03bb<\/mi>)<\/mo><\/mtd><\/mtr><\/mtable><\/math>\n\n

\u53c8\u56e0\u4e3a\u03bb<\/mi>k<\/mi><\/msub>\\lambda_{k}<\/annotation><\/semantics><\/math>\u662fk<\/mi>k<\/annotation><\/semantics><\/math>\u91cd\u6839\uff0c\u6240\u4ee5|<\/mo>A<\/mi>\u2212<\/mo>\u03bb<\/mi>E<\/mi>|<\/mo><\/mrow>=<\/mo>(<\/mo>\u03bb<\/mi>k<\/mi><\/msub>\u2212<\/mo>\u03bb<\/mi>)<\/mo><\/mrow>k<\/mi><\/msup>f<\/mi>(<\/mo>\u03bb<\/mi>)<\/mo><\/mrow><\/mrow>|A-\\lambda E|=(\\lambda_{k}-\\lambda)^kf(\\lambda)<\/annotation><\/semantics><\/math> \uff0c\u6240\u4ee5\uff0c\u51e0\u4f55\u91cd\u6570m<\/mi>m<\/annotation><\/semantics><\/math>\u5fc5\u5c0f\u4e8e\u4ee3\u6570\u91cd\u6570k<\/mi>k<\/annotation><\/semantics><\/math> , \u5373m<\/mi>\u2264<\/mo>k<\/mi><\/mrow>m\\leq k<\/annotation><\/semantics><\/math>\u3002<\/p>\n

\u53c8\u56e0\u4e3aP<\/mi>P<\/annotation><\/semantics><\/math>\u4e3a\u9149\u77e9\u9635\uff0c\u6240\u4ee5 B<\/mi>H<\/mi><\/msup><\/mtd>=<\/mo>(<\/mo>P<\/mi>H<\/mi><\/msup>A<\/mi>P<\/mi>)<\/mo><\/mrow>H<\/mi><\/msup><\/mtd><\/mtr><\/mtd>=<\/mo>(<\/mo>P<\/mi>H<\/mi><\/msup>(<\/mo>A<\/mi>P<\/mi>)<\/mo><\/mrow>)<\/mo><\/mrow>H<\/mi><\/msup><\/mtd><\/mtr><\/mtd>=<\/mo>(<\/mo>A<\/mi>P<\/mi>)<\/mo><\/mrow>H<\/mi><\/msup>(<\/mo>P<\/mi>H<\/mi><\/msup>)<\/mo><\/mrow>H<\/mi><\/msup><\/mtd><\/mtr><\/mtd>=<\/mo>(<\/mo>A<\/mi>P<\/mi>)<\/mo><\/mrow>H<\/mi><\/msup>P<\/mi><\/mtd><\/mtr><\/mtd>=<\/mo>P<\/mi>H<\/mi><\/msup>A<\/mi>H<\/mi><\/msup>P<\/mi><\/mtd><\/mtr><\/mtable>\n\\begin{aligned}\nB^H&=(P^HAP)^H \\\\\n&=(P^H(AP))^H \\\\\n&=(AP)^H(P^H)^H \\\\\n&=(AP)^HP \\\\\n&=P^HA^HP \\\\\n\\end{aligned}\n<\/annotation><\/semantics><\/math><\/p>\n

\u5982\u679cA<\/mi>A<\/annotation><\/semantics><\/math>\u4e3a\u5384\u7c73\u7279\u77e9\u9635\uff0c\u5219B<\/mi>H<\/mi><\/msup>=<\/mo>B<\/mi><\/mrow>B^H=B<\/annotation><\/semantics><\/math>\uff0c\u6240\u4ee5B<\/mi>B<\/annotation><\/semantics><\/math>\u4e5f\u4e3a\u5384\u7c73\u7279\u77e9\u9635\u3002\u6240\u4ee5B<\/mi>B<\/annotation><\/semantics><\/math>\u5fc5\u4e3a\u5bf9\u89d2\u77e9\u9635\u3002 \u6240\u4ee5\uff0cb.1\u60c5\u51b5\u4e00\u5b9a\u53ef\u4ee5\u5bf9\u89d2\u5316\u3002<\/p>\n

\u53c2\u8003\uff1a
\n1. \u5384\u7c73\u7279\u77e9\u9635<\/a> \n
\n2. \u8212\u5c14\u5b9a\u7406<\/a>
\n3. \u51e0\u4f55\u91cd\u6570\u5c0f\u4e8e\u7b49\u4e8e\u4ee3\u6570\u91cd\u6570<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"

\u4e00\u3001\u4ec0\u4e48\u6837\u7684n\u9636\u77e9\u9635\u624d\u80fd\u5bf9\u89d2\u5316\uff1f \u5148\u8bf4\u7ed3\u8bba {a.\u7279\u5f81\u503c\u65e0\u91cd\u6839\u2705b.\u6709\u91cd\u6839{b.1.\u5384\u7c73\u7279\u77e9\u9635(Hermiti … <\/p>\n

\u7ee7\u7eed\u9605\u8bfb\u201c\u77e9\u9635\u5bf9\u89d2\u5316\u201d<\/span><\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[91],"tags":[90],"class_list":["post-1605","post","type-post","status-publish","format-standard","hentry","category-91","tag-90"],"_links":{"self":[{"href":"https:\/\/thereisno.top\/index.php?rest_route=\/wp\/v2\/posts\/1605","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/thereisno.top\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/thereisno.top\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/thereisno.top\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/thereisno.top\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=1605"}],"version-history":[{"count":10,"href":"https:\/\/thereisno.top\/index.php?rest_route=\/wp\/v2\/posts\/1605\/revisions"}],"predecessor-version":[{"id":1666,"href":"https:\/\/thereisno.top\/index.php?rest_route=\/wp\/v2\/posts\/1605\/revisions\/1666"}],"wp:attachment":[{"href":"https:\/\/thereisno.top\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=1605"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/thereisno.top\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=1605"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/thereisno.top\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=1605"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}