{"id":1616,"date":"2024-12-05T00:38:49","date_gmt":"2024-12-04T16:38:49","guid":{"rendered":"https:\/\/thereisno.top\/?p=1616"},"modified":"2024-12-07T20:59:09","modified_gmt":"2024-12-07T12:59:09","slug":"%e4%ba%8c%e6%ac%a1%e5%9e%8b%e4%b8%8e%e7%9f%a9%e9%98%b5%e5%af%b9%e5%ba%94%e5%85%b3%e7%b3%bb","status":"publish","type":"post","link":"https:\/\/thereisno.top\/?p=1616","title":{"rendered":"\u4e8c\u6b21\u578b\u4e0e\u77e9\u9635\u5bf9\u5e94\u5173\u7cfb"},"content":{"rendered":"\n

f<\/mi>(<\/mo>x<\/mi>)<\/mo><\/mtd><\/mi>=<\/mo>a<\/mi>11<\/mn><\/mrow><\/msub>x<\/mi>1<\/mn>2<\/mn><\/msubsup>+<\/mo>a<\/mi>22<\/mn><\/mrow><\/msub>x<\/mi>2<\/mn>2<\/mn><\/msubsup>+<\/mo>\u22ef<\/mo>+<\/mo>a<\/mi>n<\/mi>n<\/mi><\/mrow><\/msub>x<\/mi>n<\/mi>2<\/mn><\/msubsup><\/mtd><\/mtr><\/mtd><\/mi>+<\/mo>2<\/mn>a<\/mi>12<\/mn><\/mrow><\/msub>x<\/mi>1<\/mn><\/msub>x<\/mi>2<\/mn><\/msub>+<\/mo>2<\/mn>a<\/mi>13<\/mn><\/mrow><\/msub>x<\/mi>1<\/mn><\/msub>x<\/mi>3<\/mn><\/msub>+<\/mo>\u22ef<\/mo>+<\/mo>2<\/mn>a<\/mi>n<\/mi>\u2212<\/mo>1<\/mn>,<\/mo>n<\/mi><\/mrow><\/msub>x<\/mi>n<\/mi>\u2212<\/mo>1<\/mn><\/mrow><\/msub>x<\/mi>n<\/mi><\/msub><\/mtd><\/mtr><\/mtable><\/math>\n\u89c2\u5bdf\u5404\u4e2a\u9879\uff0c\u884c\u548c\u5217\u6309x<\/mi>1<\/mn><\/msub>,<\/mo>x<\/mi>2<\/mn><\/msub>,<\/mo>x<\/mi>3<\/mn><\/msub>,<\/mo>\u22ef<\/mi>,<\/mo>x<\/mi>n<\/mi><\/msub><\/mrow>x_1,x_2,x_3,\\cdots,x_n<\/annotation><\/semantics><\/math>\u7684\u987a\u5e8f\u6392\u5217\u6210\u8868\u683c\uff0c\u6bcf\u4e2a\u683c\u5b50\u5185\u4e3a\u884c\u5217\u76f8\u4e58\u7684\u9879\uff0c\u5e73\u65b9\u9879\u6070\u5728\u5bf9\u89d2\u7ebf\u4f4d\u7f6e\uff0c\u5176\u4ed6\u9879\u653e\u5728\u5bf9\u89d2\u7ebf\u4e0a\u4e09\u89d2\u533a\u57df\uff0c\u53ef\u4ee5\u5f97\u5230\u4e0b\u9762\u65b9\u9635\uff1a \n\n<\/mtd>x<\/mi>1<\/mn><\/msub><\/mtd>x<\/mi>2<\/mn><\/msub><\/mtd>x<\/mi>3<\/mn><\/msub><\/mtd>\u22ef<\/mo><\/mtd>x<\/mi>n<\/mi><\/msub><\/mtd><\/mtr>x<\/mi>1<\/mn><\/msub><\/mtd>a<\/mi>11<\/mn><\/mrow><\/msub>x<\/mi>1<\/mn>2<\/mn><\/msubsup><\/mtd>2<\/mn>a<\/mi>12<\/mn><\/mrow><\/msub>x<\/mi>1<\/mn><\/msub>x<\/mi>2<\/mn><\/msub><\/mtd>2<\/mn>a<\/mi>13<\/mn><\/mrow><\/msub>x<\/mi>1<\/mn><\/msub>x<\/mi>3<\/mn><\/msub><\/mtd>\u22ef<\/mo><\/mtd>2<\/mn>a<\/mi>1<\/mn>n<\/mi><\/mrow><\/msub>x<\/mi>1<\/mn><\/msub>x<\/mi>n<\/mi><\/msub><\/mtd><\/mtr>x<\/mi>2<\/mn><\/msub><\/mtd>0<\/mn><\/mtd>a<\/mi>22<\/mn><\/mrow><\/msub>x<\/mi>2<\/mn>2<\/mn><\/msubsup><\/mtd>2<\/mn>a<\/mi>23<\/mn><\/mrow><\/msub>x<\/mi>2<\/mn><\/msub>x<\/mi>3<\/mn><\/msub><\/mtd>\u22ef<\/mo><\/mtd>2<\/mn>a<\/mi>2<\/mn>n<\/mi><\/mrow><\/msub>x<\/mi>2<\/mn><\/msub>x<\/mi>n<\/mi><\/msub><\/mtd><\/mtr>x<\/mi>3<\/mn><\/msub><\/mtd>0<\/mn><\/mtd>0<\/mn><\/mtd>a<\/mi>33<\/mn><\/mrow><\/msub>x<\/mi>3<\/mn>2<\/mn><\/msubsup><\/mtd>\u22ef<\/mo><\/mtd>2<\/mn>a<\/mi>3<\/mn>n<\/mi><\/mrow><\/msub>x<\/mi>3<\/mn><\/msub>x<\/mi>n<\/mi><\/msub><\/mtd><\/mtr>\u22ee<\/mo><\/mrow><\/mtd>\u22ee<\/mo><\/mrow><\/mtd>\u22ee<\/mo><\/mrow><\/mtd>\u22f1<\/mo><\/mtd>\u22ee<\/mo><\/mrow><\/mtd><\/mtr>x<\/mi>n<\/mi><\/msub><\/mtd>0<\/mn><\/mtd>0<\/mn><\/mtd>0<\/mn><\/mtd>\u22ef<\/mo><\/mtd>a<\/mi>n<\/mi>n<\/mi><\/mrow><\/msub>x<\/mi>n<\/mi>2<\/mn><\/msubsup><\/mtd><\/mtr><\/mtable><\/mtd><\/mtr><\/mtable><\/math>\n\n\u5982\u679c\u628a\u50cf 2<\/mn>a<\/mi>12<\/mn><\/msub>,<\/mo>2<\/mn>a<\/mi>13<\/mn><\/msub>,<\/mo>\u2026<\/mi>,<\/mo>2<\/mn>a<\/mi>(<\/mo>n<\/mi>\u2212<\/mo>1<\/mn>)<\/mo><\/mrow>n<\/mi><\/mrow><\/msub><\/mrow>2a_{12} , 2a_{13},\\dots,2a_{(n-1)n}<\/annotation><\/semantics><\/math> \u8fd9\u6837\u76842\u500d\u7684\u7cfb\u6570\u6cbf\u7740\u5bf9\u89d2\u7ebf\u5bf9\u79f0\u7684\u4f4d\u7f6e\u62c6\u5206\u653e\u7f6e\uff0c\u5373a<\/mi>12<\/mn><\/msub>=<\/mo>a<\/mi>21<\/mn><\/msub>,<\/mo>a<\/mi>13<\/mn><\/msub>=<\/mo>a<\/mi>31<\/mn><\/msub>,<\/mo>\u2026<\/mi>,<\/mo>a<\/mi>(<\/mo>n<\/mi>\u2212<\/mo>1<\/mn>)<\/mo><\/mrow>n<\/mi><\/mrow><\/msub>=<\/mo>a<\/mi>n<\/mi>(<\/mo>n<\/mi>\u2212<\/mo>1<\/mn>)<\/mo><\/mrow><\/mrow><\/msub><\/mrow>a_{12}=a_{21} , a_{13}=a_{31},\\dots,a_{(n-1)n}=a_{n(n-1)}<\/annotation><\/semantics><\/math>\uff0c\u90a3\u4e48\u53ef\u4ee5\u5f97\u5230\u4e0b\u9762\u7684\u6837\u5b50\uff1a<\/p>\n\n\n\n\n\n\n\n

\n <\/mtd>x<\/mi>1<\/mn><\/msub><\/mtd>x<\/mi>2<\/mn><\/msub><\/mtd>x<\/mi>3<\/mn><\/msub><\/mtd>\u22ef<\/mo><\/mtd>x<\/mi>n<\/mi><\/msub><\/mtd><\/mtr>x<\/mi>1<\/mn><\/msub><\/mtd>a<\/mi>11<\/mn><\/mrow><\/msub>x<\/mi>1<\/mn>2<\/mn><\/msubsup><\/mtd>a<\/mi>12<\/mn><\/mrow><\/msub>x<\/mi>1<\/mn><\/msub>x<\/mi>2<\/mn><\/msub><\/mtd>a<\/mi>13<\/mn><\/mrow><\/msub>x<\/mi>1<\/mn><\/msub>x<\/mi>3<\/mn><\/msub><\/mtd>\u22ef<\/mo><\/mtd>a<\/mi>1<\/mn>n<\/mi><\/mrow><\/msub>x<\/mi>1<\/mn><\/msub>x<\/mi>n<\/mi><\/msub><\/mtd><\/mtr>x<\/mi>2<\/mn><\/msub><\/mtd>a<\/mi>21<\/mn><\/mrow><\/msub>x<\/mi>1<\/mn><\/msub>x<\/mi>2<\/mn><\/msub><\/mtd>a<\/mi>22<\/mn><\/mrow><\/msub>x<\/mi>2<\/mn>2<\/mn><\/msubsup><\/mtd>a<\/mi>23<\/mn><\/mrow><\/msub>x<\/mi>2<\/mn><\/msub>x<\/mi>3<\/mn><\/msub><\/mtd>\u22ef<\/mo><\/mtd>a<\/mi>2<\/mn>n<\/mi><\/mrow><\/msub>x<\/mi>2<\/mn><\/msub>x<\/mi>n<\/mi><\/msub><\/mtd><\/mtr>x<\/mi>3<\/mn><\/msub><\/mtd>a<\/mi>31<\/mn><\/mrow><\/msub>x<\/mi>1<\/mn><\/msub>x<\/mi>3<\/mn><\/msub><\/mtd>a<\/mi>32<\/mn><\/mrow><\/msub>x<\/mi>2<\/mn><\/msub>x<\/mi>3<\/mn><\/msub><\/mtd>a<\/mi>33<\/mn><\/mrow><\/msub>x<\/mi>3<\/mn>2<\/mn><\/msubsup><\/mtd>\u22ef<\/mo><\/mtd>a<\/mi>3<\/mn>n<\/mi><\/mrow><\/msub>x<\/mi>3<\/mn><\/msub>x<\/mi>n<\/mi><\/msub><\/mtd><\/mtr>\u22ee<\/mo><\/mrow><\/mtd>\u22ee<\/mo><\/mrow><\/mtd>\u22ee<\/mo><\/mrow><\/mtd>\u22f1<\/mo><\/mtd>\u22ee<\/mo><\/mrow><\/mtd><\/mtr>x<\/mi>n<\/mi><\/msub><\/mtd>a<\/mi>n<\/mi>1<\/mn><\/mrow><\/msub>x<\/mi>1<\/mn><\/msub>x<\/mi>n<\/mi><\/msub><\/mtd>a<\/mi>n<\/mi>2<\/mn><\/mrow><\/msub>x<\/mi>2<\/mn><\/msub>x<\/mi>n<\/mi><\/msub><\/mtd>a<\/mi>n<\/mi>3<\/mn><\/mrow><\/msub>x<\/mi>3<\/mn><\/msub>x<\/mi>n<\/mi><\/msub><\/mtd>\u22ef<\/mo><\/mtd>a<\/mi>n<\/mi>n<\/mi><\/mrow><\/msub>x<\/mi>n<\/mi>2<\/mn><\/msubsup><\/mtd><\/mtr><\/mtable><\/mtd><\/mtr><\/mtable><\/math>\n\u5373 f<\/mi>(<\/mo>x<\/mi>)<\/mo><\/mrow><\/mtd>=<\/mo>x<\/mi>1<\/mn><\/msub>(<\/mo>a<\/mi>11<\/mn><\/msub>x<\/mi>1<\/mn><\/msub>+<\/mo>a<\/mi>12<\/mn><\/msub>x<\/mi>2<\/mn><\/msub>+<\/mo>\u22ef<\/mi>+<\/mo>a<\/mi>1<\/mn>n<\/mi><\/mrow><\/msub>x<\/mi>n<\/mi><\/msub><\/mtd><\/mtr><\/mtd>+<\/mo>x<\/mi>2<\/mn><\/msub>(<\/mo>a<\/mi>21<\/mn><\/msub>x<\/mi>1<\/mn><\/msub>+<\/mo>a<\/mi>22<\/mn><\/msub>x<\/mi>2<\/mn><\/msub>+<\/mo>\u22ef<\/mi>+<\/mo>a<\/mi>2<\/mn>n<\/mi><\/mrow><\/msub>x<\/mi>n<\/mi><\/msub>)<\/mo><\/mrow><\/mtd><\/mtr><\/mtd>+<\/mo>x<\/mi>3<\/mn><\/msub>(<\/mo>a<\/mi>31<\/mn><\/msub>x<\/mi>1<\/mn><\/msub>+<\/mo>a<\/mi>32<\/mn><\/msub>x<\/mi>2<\/mn><\/msub>+<\/mo>\u22ef<\/mi>+<\/mo>a<\/mi>3<\/mn>n<\/mi><\/mrow><\/msub>x<\/mi>n<\/mi><\/msub>)<\/mo><\/mrow><\/mtd><\/mtr><\/mtd>+<\/mo>\u22ef<\/mi><\/mtd><\/mtr><\/mtd>+<\/mo>x<\/mi>n<\/mi><\/msub>(<\/mo>a<\/mi>n<\/mi>1<\/mn><\/mrow><\/msub>x<\/mi>1<\/mn><\/msub>+<\/mo>a<\/mi>n<\/mi>2<\/mn><\/mrow><\/msub>x<\/mi>2<\/mn><\/msub>+<\/mo>\u22ef<\/mi>+<\/mo>a<\/mi>n<\/mi>n<\/mi><\/mrow><\/msub>x<\/mi>n<\/mi><\/msub>)<\/mo><\/mrow><\/mtd><\/mtr><\/mtable>\n\\begin{aligned}\nf(x) &=x_1(a_{11}x_1 + a_{12}x_2 + \\cdots + a_{1n}x_n \\\\\n& +x_2(a_{21}x_1 + a_{22}x_2 + \\cdots + a_{2n}x_n) \\\\\n& +x_3(a_{31}x_1 + a_{32}x_2 + \\cdots + a_{3n}x_n) \\\\ \n& + \\cdots\\\\\n& + x_n(a_{n1}x_1 + a_{n2}x_2 + \\cdots + a_{nn}x_n) \\\\\n\\end{aligned}\n<\/annotation><\/semantics><\/math> \u5199\u6210\u77e9\u9635\u76f8\u4e58\u7684\u65b9\u5f0f\u4e3a\uff1a f<\/mi>(<\/mo>x<\/mi>)<\/mo><\/mrow><\/mtd>=<\/mo>(<\/mo>x<\/mi>1<\/mn><\/msub>,<\/mo>x<\/mi>2<\/mn><\/msub>,<\/mo>\u22ef<\/mi>,<\/mo>x<\/mi>n<\/mi><\/msub>)<\/mo><\/mrow>(<\/mo>a<\/mi>11<\/mn><\/msub>x<\/mi>1<\/mn><\/msub><\/mtd>a<\/mi>12<\/mn><\/msub>x<\/mi>2<\/mn><\/msub><\/mtd>\u22ef<\/mi><\/mtd>a<\/mi>1<\/mn>n<\/mi><\/mrow><\/msub>x<\/mi>n<\/mi><\/msub><\/mtd><\/mtr>a<\/mi>21<\/mn><\/msub>x<\/mi>1<\/mn><\/msub><\/mtd>a<\/mi>22<\/mn><\/msub>x<\/mi>2<\/mn><\/msub><\/mtd>\u22ef<\/mi><\/mtd>a<\/mi>2<\/mn>n<\/mi><\/mrow><\/msub>x<\/mi>n<\/mi><\/msub><\/mtd><\/mtr>\u22ee<\/mi><\/mtd>\u22ee<\/mi><\/mtd>\u22f1<\/mi><\/mtd>\u22ee<\/mi><\/mtd><\/mtr>a<\/mi>n<\/mi>1<\/mn><\/mrow><\/msub>x<\/mi>1<\/mn><\/msub><\/mtd>a<\/mi>n<\/mi>2<\/mn><\/mrow><\/msub>x<\/mi>2<\/mn><\/msub><\/mtd>\u22ef<\/mi><\/mtd>a<\/mi>n<\/mi>n<\/mi><\/mrow><\/msub>x<\/mi>n<\/mi><\/msub><\/mtd><\/mtr><\/mtable>)<\/mo><\/mrow><\/mtd><\/mtr><\/mtd>=<\/mo>(<\/mo>x<\/mi>1<\/mn><\/msub>,<\/mo>x<\/mi>2<\/mn><\/msub>,<\/mo>\u22ef<\/mi>,<\/mo>x<\/mi>n<\/mi><\/msub>)<\/mo><\/mrow>(<\/mo>a<\/mi>11<\/mn><\/msub><\/mtd>a<\/mi>12<\/mn><\/msub><\/mtd>\u22ef<\/mi><\/mtd>a<\/mi>1<\/mn>n<\/mi><\/mrow><\/msub><\/mtd><\/mtr>a<\/mi>21<\/mn><\/msub><\/mtd>a<\/mi>22<\/mn><\/msub><\/mtd>\u22ef<\/mi><\/mtd>a<\/mi>2<\/mn>n<\/mi><\/mrow><\/msub><\/mtd><\/mtr>\u22ee<\/mi><\/mtd>\u22ee<\/mi><\/mtd>\u22f1<\/mi><\/mtd>\u22ee<\/mi><\/mtd><\/mtr>a<\/mi>n<\/mi>1<\/mn><\/mrow><\/msub><\/mtd>a<\/mi>n<\/mi>2<\/mn><\/mrow><\/msub><\/mtd>\u22ef<\/mi><\/mtd>a<\/mi>n<\/mi>n<\/mi><\/mrow><\/msub><\/mtd><\/mtr><\/mtable>)<\/mo><\/mrow>(<\/mo>x<\/mi>1<\/mn><\/msub><\/mtd><\/mtr>x<\/mi>2<\/mn><\/msub><\/mtd><\/mtr>\u22ee<\/mi><\/mtd><\/mtr>x<\/mi>n<\/mi><\/msub><\/mtd><\/mtr><\/mtable>)<\/mo><\/mrow><\/mtd><\/mtr><\/mtd>=<\/mo>x<\/mi>T<\/mi><\/msup>A<\/mi>x<\/mi><\/mtd><\/mtr><\/mtable>\n\\begin{aligned}\nf(x)&= (x_1, x_2, \\cdots, x_n) \\begin{pmatrix}a_{11}x_1 & a_{12}x_2 & \\cdots & a_{1n}x_n \\\\ a_{21}x_1 & a_{22}x_2 & \\cdots & a_{2n}x_n \\\\ \\vdots & \\vdots & \\ddots & \\vdots \\\\ a_{n1}x_1 & a_{n2}x_2 & \\cdots & a_{nn}x_n \\end{pmatrix}\\\\\n&=(x_1, x_2, \\cdots, x_n)\\begin{pmatrix}a_{11} & a_{12} & \\cdots & a_{1n} \\\\ a_{21} & a_{22} & \\cdots & a_{2n} \\\\ \\vdots & \\vdots & \\ddots & \\vdots \\\\ a_{n1} & a_{n2} & \\cdots & a_{nn} \\end{pmatrix}\\begin{pmatrix}x_1 \\\\ x_2 \\\\ \\vdots \\\\ x_n \\end{pmatrix} \\\\\n&=x^TAx\n\\end{aligned}\n<\/annotation><\/semantics><\/math> \u5176\u4e2d A<\/mi>=<\/mo>(<\/mo>a<\/mi>11<\/mn><\/msub><\/mtd>a<\/mi>12<\/mn><\/msub><\/mtd>\u22ef<\/mi><\/mtd>a<\/mi>1<\/mn>n<\/mi><\/mrow><\/msub><\/mtd><\/mtr>a<\/mi>21<\/mn><\/msub><\/mtd>a<\/mi>22<\/mn><\/msub><\/mtd>\u22ef<\/mi><\/mtd>a<\/mi>2<\/mn>n<\/mi><\/mrow><\/msub><\/mtd><\/mtr>\u22ee<\/mi><\/mtd>\u22ee<\/mi><\/mtd>\u22f1<\/mi><\/mtd>\u22ee<\/mi><\/mtd><\/mtr>a<\/mi>n<\/mi>1<\/mn><\/mrow><\/msub><\/mtd>a<\/mi>n<\/mi>2<\/mn><\/mrow><\/msub><\/mtd>\u22ef<\/mi><\/mtd>a<\/mi>n<\/mi>n<\/mi><\/mrow><\/msub><\/mtd><\/mtr><\/mtable>)<\/mo><\/mrow>,<\/mo>x<\/mi>=<\/mo>(<\/mo>x<\/mi>1<\/mn><\/msub><\/mtd><\/mtr>x<\/mi>2<\/mn><\/msub><\/mtd><\/mtr>\u22ee<\/mi><\/mtd><\/mtr>x<\/mi>n<\/mi><\/msub><\/mtd><\/mtr><\/mtable>)<\/mo><\/mrow><\/mrow>\nA=\\begin{pmatrix}a_{11} & a_{12} & \\cdots & a_{1n} \\\\ a_{21} & a_{22} & \\cdots & a_{2n} \\\\ \\vdots & \\vdots & \\ddots & \\vdots \\\\ a_{n1} & a_{n2} & \\cdots & a_{nn} \\end{pmatrix} , x=\\begin{pmatrix}x_1 \\\\ x_2 \\\\ \\vdots \\\\ x_n \\end{pmatrix}\n<\/annotation><\/semantics><\/math><\/p>\n

\u4e8c\u6b21\u578bf<\/mi>(<\/mo>x<\/mi>)<\/mo><\/mrow><\/mrow>f(x)<\/annotation><\/semantics><\/math>\uff0c\u548c\u77e9\u9635\u8868\u793ax<\/mi>T<\/mi><\/msup>A<\/mi>x<\/mi><\/mrow>x^TAx<\/annotation><\/semantics><\/math>\u662f\u7b49\u4ef7\u7684\u3002\u4e8c\u6b21\u578b\u53ef\u4ee5\u901a\u8fc7\u914d\u65b9\u6cd5\u6362\u5143\u6807\u51c6\u5316\u3002\u7136\u800c\uff0c\u53ea\u6709\u8868\u793a\u6210\u5bf9\u79f0\u77e9\u9635<\/strong>\u624d\u53ef\u4ee5\u7684\u5bf9\u89d2\u5316\u4e3a\u6807\u51c6\u5f62\u3002<\/p>\n

\u90a3\u4e48\u600e\u4e48\u7406\u89e3\u4e8c\u6b21\u578b\u5982\u679c\u8868\u793a\u4e3a\u975e\u5bf9\u79f0\u77e9\u9635\u4e3a\u4ec0\u4e48\u4e0d\u80fd\u5bf9\u89d2\u5316\u5462\uff1f\u660e\u660e\u662f\u7b49\u4ef7\u7684\u8868\u793a\u3002\u4f8b\u5982\uff0c x<\/mi>1<\/mn>2<\/mn><\/msubsup>+<\/mo>x<\/mi>2<\/mn>2<\/mn><\/msubsup>+<\/mo>2<\/mn>x<\/mi>1<\/mn><\/msub>x<\/mi>2<\/mn><\/msub><\/mrow>x_1^2 + x_2^2 + 2x_1x_2<\/annotation><\/semantics><\/math>\u5982\u679c\u8868\u793a\u4e3a A<\/mi>=<\/mo>(<\/mo>1<\/mn><\/mtd>1<\/mn><\/mtd><\/mtr>1<\/mn><\/mtd>1<\/mn><\/mtd><\/mtr><\/mtable>)<\/mo><\/mrow><\/mtd><\/mtr>B<\/mi>=<\/mo>(<\/mo>1<\/mn><\/mtd>2<\/mn><\/mtd><\/mtr>0<\/mn><\/mtd>1<\/mn><\/mtd><\/mtr><\/mtable>)<\/mo><\/mrow><\/mtd><\/mtr>C<\/mi>=<\/mo>(<\/mo>1<\/mn><\/mtd>0<\/mn><\/mtd><\/mtr>2<\/mn><\/mtd>1<\/mn><\/mtd><\/mtr><\/mtable>)<\/mo><\/mrow><\/mtd><\/mtr><\/mtable>\n\\begin{aligned}\nA=\\begin{pmatrix}\n1 & 1 \\\\\n1 & 1\n\\end{pmatrix} \\\\\nB=\\begin{pmatrix}\n1 & 2 \\\\\n0 & 1\n\\end{pmatrix}\\\\\nC=\\begin{pmatrix}\n1 & 0 \\\\\n2 & 1\n\\end{pmatrix}\n\\end{aligned}\n<\/annotation><\/semantics><\/math> B\u548cC\u53ea\u662f\u4ea4\u6362\u4e86\u4f4d\u7f6e\uff0c\u53ea\u8ba8\u8bbaA\u3001B\u4e24\u4e2a\u77e9\u9635\u7684\u5bf9\u89d2\u5316\u3002\u5176\u7279\u5f81\u503c\u5206\u522b\u4e3a0\u62162\u3001\u91cd\u68391\u3002<\/p>\n

A\u7684\u7279\u5f81\u503c\u4e3a2\u30010\uff0c\u7279\u5f81\u5411\u91cf\u5206\u522b\u4e3a\uff1a (<\/mo>1<\/mn><\/mtd><\/mtr>1<\/mn><\/mtd><\/mtr><\/mtable>)<\/mo><\/mrow>,<\/mo>(<\/mo>\u2212<\/mo>1<\/mn><\/mtd><\/mtr>1<\/mn><\/mtd><\/mtr><\/mtable>)<\/mo><\/mrow><\/mrow>\n\\begin{pmatrix}1 \\\\ 1\\end{pmatrix},\n\\begin{pmatrix}-1 \\\\ 1\\end{pmatrix}\n<\/annotation><\/semantics><\/math> \u6240\u4ee5\uff0c P<\/mi><\/mtd>=<\/mo>(<\/mo>1<\/mn><\/mtd>\u2212<\/mo>1<\/mn><\/mtd><\/mtr>1<\/mn><\/mtd>1<\/mn><\/mtd><\/mtr><\/mtable>)<\/mo><\/mrow><\/mtd><\/mtr>P<\/mi>\u2212<\/mo>1<\/mn><\/mrow><\/msup><\/mtd>=<\/mo>(<\/mo>1<\/mn>2<\/mn><\/mfrac><\/mtd>1<\/mn>2<\/mn><\/mfrac><\/mtd><\/mtr>1<\/mn>2<\/mn><\/mfrac><\/mtd>\u2212<\/mo>1<\/mn>2<\/mn><\/mfrac><\/mtd><\/mtr><\/mtable>)<\/mo><\/mrow><\/mtd><\/mtr><\/mtable>\n\\begin{aligned}\nP&=\\begin{pmatrix}1 & -1 \\\\ 1 & 1\\end{pmatrix} \\\\\nP^{-1}&=\\begin{pmatrix}\\frac{1}{2} & \\frac{1}{2} \\\\ \\frac{1}{2} & -\\frac{1}{2}\\end{pmatrix}\\\\\n\\end{aligned}\n<\/annotation><\/semantics><\/math> \u90a3\u4e48\uff0c P<\/mi>\u2212<\/mo>1<\/mn><\/mrow><\/msup>A<\/mi>P<\/mi><\/mtd>=<\/mo>(<\/mo>1<\/mn>2<\/mn><\/mfrac><\/mtd>1<\/mn>2<\/mn><\/mfrac><\/mtd><\/mtr>1<\/mn>2<\/mn><\/mfrac><\/mtd>\u2212<\/mo>1<\/mn>2<\/mn><\/mfrac><\/mtd><\/mtr><\/mtable>)<\/mo><\/mrow>(<\/mo>1<\/mn><\/mtd>1<\/mn><\/mtd><\/mtr>1<\/mn><\/mtd>1<\/mn><\/mtd><\/mtr><\/mtable>)<\/mo><\/mrow>(<\/mo>1<\/mn><\/mtd>\u2212<\/mo>1<\/mn><\/mtd><\/mtr>1<\/mn><\/mtd>1<\/mn><\/mtd><\/mtr><\/mtable>)<\/mo><\/mrow><\/mtd><\/mtr><\/mtd>=<\/mo>(<\/mo>2<\/mn><\/mtd>0<\/mn><\/mtd><\/mtr>0<\/mn><\/mtd>0<\/mn><\/mtd><\/mtr><\/mtable>)<\/mo><\/mrow><\/mtd><\/mtr><\/mtable>\n\\begin{aligned}\nP^{-1}AP&=\\begin{pmatrix}\\frac{1}{2} & \\frac{1}{2} \\\\ \\frac{1}{2} & -\\frac{1}{2}\\end{pmatrix}\\begin{pmatrix}1 & 1 \\\\ 1 & 1\\end{pmatrix}\\begin{pmatrix}1 & -1 \\\\ 1 & 1\\end{pmatrix}\\\\\n&=\\begin{pmatrix}2 & 0 \\\\ 0 & 0\\end{pmatrix}\n\\end{aligned}\n<\/annotation><\/semantics><\/math> \u82e5x<\/mi>=<\/mo>P<\/mi>y<\/mi><\/mrow>x=Py<\/annotation><\/semantics><\/math>\uff0cx<\/mi>T<\/mi><\/msup>=<\/mo>(<\/mo>P<\/mi>y<\/mi>)<\/mo><\/mrow>T<\/mi><\/msup>=<\/mo>y<\/mi>T<\/mi><\/msup>P<\/mi>T<\/mi><\/msup><\/mrow>x^T=(Py)^T=y^TP^T<\/annotation><\/semantics><\/math>\u3002<\/p>\n

\u4f46\u7531\u4e8e\u6b64\u65f6\u7684P<\/mi>P<\/annotation><\/semantics><\/math>\u672a\u7ecf\u9149\u53d8\u6362\uff0cP<\/mi>\u2212<\/mo>1<\/mn><\/mrow><\/msup>\u2260<\/mo>P<\/mi>T<\/mi><\/msup><\/mrow>P^{-1}\\neq P^T<\/annotation><\/semantics><\/math>\uff0c\u6240\u4ee5y<\/mi>T<\/mi><\/msup>(<\/mo>P<\/mi>\u2212<\/mo>1<\/mn><\/mrow><\/msup>A<\/mi>P<\/mi>)<\/mo><\/mrow>y<\/mi>\u2260<\/mo>d<\/mi>i<\/mi>a<\/mi>g<\/mi>(<\/mo>2<\/mn>,<\/mo>0<\/mn>)<\/mo><\/mrow><\/mrow>y^T(P^{-1}AP)y\\neq diag(2,0)<\/annotation><\/semantics><\/math><\/p>\n

\u5c06P<\/mi>P<\/annotation><\/semantics><\/math>\u77e9\u9635\u8f6c\u6362\u4e3a\u9149\u53d8\u6362\uff0c<\/p>\n

U<\/mi><\/mtd>=<\/mo>(<\/mo>1<\/mn>2<\/mn><\/msqrt><\/mfrac><\/mtd>\u2212<\/mo>1<\/mn>2<\/mn><\/msqrt><\/mfrac><\/mtd><\/mtr>1<\/mn>2<\/mn><\/msqrt><\/mfrac><\/mtd>1<\/mn>2<\/mn><\/msqrt><\/mfrac><\/mtd><\/mtr><\/mtable>)<\/mo><\/mrow><\/mtd><\/mtr>U<\/mi>\u2212<\/mo>1<\/mn><\/mrow><\/msup><\/mtd>=<\/mo>(<\/mo>1<\/mn>2<\/mn><\/msqrt><\/mfrac><\/mtd>1<\/mn>2<\/mn><\/msqrt><\/mfrac><\/mtd><\/mtr>\u2212<\/mo>1<\/mn>2<\/mn><\/msqrt><\/mfrac><\/mtd>1<\/mn>2<\/mn><\/msqrt><\/mfrac><\/mtd><\/mtr><\/mtable>)<\/mo><\/mrow><\/mtd><\/mtr><\/mtd>=<\/mo>U<\/mi>T<\/mi><\/msup><\/mtd><\/mtr><\/mtable>\n\\begin{aligned}\nU&=\\begin{pmatrix} \\frac{1}{\\sqrt{2}} & -\\frac{1}{\\sqrt{2}} \\\\ \\frac{1}{\\sqrt{2}} & \\frac{1}{\\sqrt{2}}\\end{pmatrix} \\\\\nU^{-1}&=\\begin{pmatrix}\\frac{1}{\\sqrt{2}} & \\frac{1}{\\sqrt{2}} \\\\ -\\frac{1}{\\sqrt{2}} & \\frac{1}{\\sqrt{2}}\\end{pmatrix}\\\\\n&=U^T\n\\end{aligned}\n<\/annotation><\/semantics><\/math><\/p>\n

\u5373 f<\/mi>(<\/mo>y<\/mi>1<\/mn><\/msub>,<\/mo>y<\/mi>2<\/mn><\/msub>)<\/mo><\/mrow><\/mtd>=<\/mo>2<\/mn>y<\/mi>1<\/mn>2<\/mn><\/msubsup>+<\/mo>0<\/mn>y<\/mi>2<\/mn>2<\/mn><\/msubsup><\/mtd><\/mtr><\/mtable>\n\\begin{aligned}\nf(y_1,y_2)&=2y_1^2+0y_2^2\n\\end{aligned}\n<\/annotation><\/semantics><\/math> \u6b64\u65f6\u5bf9\u5e94\u7684\u6362\u5143\u5173\u7cfb\u4e3a\uff1a (<\/mo>x<\/mi>1<\/mn><\/msub><\/mtd><\/mtr>x<\/mi>2<\/mn><\/msub><\/mtd><\/mtr><\/mtable>)<\/mo><\/mrow>=<\/mo>U<\/mi>(<\/mo>y<\/mi>1<\/mn><\/msub><\/mtd><\/mtr>y<\/mi>2<\/mn><\/msub><\/mtd><\/mtr><\/mtable>)<\/mo><\/mrow>=<\/mo>(<\/mo>1<\/mn>2<\/mn><\/msqrt><\/mfrac><\/mtd>\u2212<\/mo>1<\/mn>2<\/mn><\/msqrt><\/mfrac><\/mtd><\/mtr>1<\/mn>2<\/mn><\/msqrt><\/mfrac><\/mtd>1<\/mn>2<\/mn><\/msqrt><\/mfrac><\/mtd><\/mtr><\/mtable>)<\/mo><\/mrow>(<\/mo>y<\/mi>1<\/mn><\/msub><\/mtd><\/mtr>y<\/mi>2<\/mn><\/msub><\/mtd><\/mtr><\/mtable>)<\/mo><\/mrow><\/mtd><\/mtr>\u21d2<\/mo>{<\/mo>x<\/mi>1<\/mn><\/msub>=<\/mo>1<\/mn>2<\/mn><\/msqrt><\/mfrac>y<\/mi>1<\/mn><\/msub>\u2212<\/mo>1<\/mn>2<\/mn><\/msqrt><\/mfrac>y<\/mi>2<\/mn><\/msub><\/mtd><\/mtr>x<\/mi>2<\/mn><\/msub>=<\/mo>1<\/mn>2<\/mn><\/msqrt><\/mfrac>y<\/mi>1<\/mn><\/msub>+<\/mo>1<\/mn>2<\/mn><\/msqrt><\/mfrac>y<\/mi>2<\/mn><\/msub><\/mtd><\/mtr><\/mtable><\/mrow><\/mtd><\/mtr><\/mtable>\n\\begin{aligned}\n\\begin{pmatrix}x_1 \\\\ x_2\\end{pmatrix}=U\\begin{pmatrix}y_1 \\\\ y_2\\end{pmatrix}=\\begin{pmatrix} \\frac{1}{\\sqrt{2}} & -\\frac{1}{\\sqrt{2}} \\\\ \\frac{1}{\\sqrt{2}} & \\frac{1}{\\sqrt{2}}\\end{pmatrix}\\begin{pmatrix}y_1 \\\\ y_2\\end{pmatrix}\\\\\n\\Rightarrow\n\\left\\{\n\\begin{aligned}\nx_1=\\frac{1}{\\sqrt{2}}y_1-\\frac{1}{\\sqrt{2}}y_2 \\\\\nx_2=\\frac{1}{\\sqrt{2}}y_1+\\frac{1}{\\sqrt{2}}y_2\n\\end{aligned}\n\\right.\n\\end{aligned}\n<\/annotation><\/semantics><\/math><\/p>\n

(<\/mo>y<\/mi>1<\/mn><\/msub><\/mtd><\/mtr>y<\/mi>2<\/mn><\/msub><\/mtd><\/mtr><\/mtable>)<\/mo><\/mrow>=<\/mo>U<\/mi>\u2212<\/mo>1<\/mn><\/mrow><\/msup>(<\/mo>x<\/mi>1<\/mn><\/msub><\/mtd><\/mtr>x<\/mi>2<\/mn><\/msub><\/mtd><\/mtr><\/mtable>)<\/mo><\/mrow>=<\/mo>U<\/mi>T<\/mi><\/msup>(<\/mo>x<\/mi>1<\/mn><\/msub><\/mtd><\/mtr>x<\/mi>2<\/mn><\/msub><\/mtd><\/mtr><\/mtable>)<\/mo><\/mrow>=<\/mo>(<\/mo>1<\/mn>2<\/mn><\/msqrt><\/mfrac><\/mtd>1<\/mn>2<\/mn><\/msqrt><\/mfrac><\/mtd><\/mtr>\u2212<\/mo>1<\/mn>2<\/mn><\/msqrt><\/mfrac><\/mtd>1<\/mn>2<\/mn><\/msqrt><\/mfrac><\/mtd><\/mtr><\/mtable>)<\/mo><\/mrow>(<\/mo>x<\/mi>1<\/mn><\/msub><\/mtd><\/mtr>x<\/mi>2<\/mn><\/msub><\/mtd><\/mtr><\/mtable>)<\/mo><\/mrow><\/mtd><\/mtr>\u21d2<\/mo>{<\/mo>y<\/mi>1<\/mn><\/msub><\/mtd>=<\/mo>1<\/mn>2<\/mn><\/msqrt><\/mfrac>x<\/mi>1<\/mn><\/msub>+<\/mo>1<\/mn>2<\/mn><\/msqrt><\/mfrac>x<\/mi>2<\/mn><\/msub><\/mtd><\/mtr>y<\/mi>2<\/mn><\/msub><\/mtd>=<\/mo>\u2212<\/mo>1<\/mn>2<\/mn><\/msqrt><\/mfrac>x<\/mi>1<\/mn><\/msub>+<\/mo>1<\/mn>2<\/mn><\/msqrt><\/mfrac>x<\/mi>2<\/mn><\/msub><\/mtd><\/mtr><\/mtable><\/mrow><\/mtd><\/mtr><\/mtable>\n\\begin{aligned}\n\\begin{pmatrix}y_1 \\\\ y_2\\end{pmatrix}=U^{-1}\\begin{pmatrix}x_1 \\\\ x_2\\end{pmatrix}=U^{T}\\begin{pmatrix}x_1 \\\\ x_2\\end{pmatrix}=\\begin{pmatrix}\\frac{1}{\\sqrt{2}} & \\frac{1}{\\sqrt{2}} \\\\ -\\frac{1}{\\sqrt{2}} & \\frac{1}{\\sqrt{2}}\\end{pmatrix}\\begin{pmatrix}x_1 \\\\ x_2\\end{pmatrix}\\\\\n\\Rightarrow\n\\left\\{\n\\begin{aligned}\ny_1&=\\frac{1}{\\sqrt{2}}x_1+\\frac{1}{\\sqrt{2}}x_2 \\\\\ny_2&=-\\frac{1}{\\sqrt{2}}x_1+\\frac{1}{\\sqrt{2}}x_2\n\\end{aligned}\n\\right.\n\\end{aligned}\n<\/annotation><\/semantics><\/math><\/p>\n

\u5982\u4f55\u7406\u89e3\u8fd9\u79cd\u53d8\u6362\u5462\uff1f<\/h4>\n

\u8fd9\u79cd\u53d8\u6362\uff0c\u5c06\u5750\u6807\u8f74\u65cb\u8f6c45\u5ea6\uff0c\u5982\u4e0b\u56fe\u3002 \"\u6b63\u4ea4\u53d8\u6362\"<\/p>\n

\u4e0e\u914d\u65b9\u6cd5\u5bf9\u7167<\/h3>\n

\u5bf9\u4e8e\u4e0a\u9762\u7684\u7b80\u5355\u7684\u4e8c\u6b21\u578b\uff0c\u5f88\u663e\u7136\u53ef\u4ee5\u505ay<\/mi>1<\/mn><\/msub>=<\/mo>x<\/mi>1<\/mn><\/msub>+<\/mo>x<\/mi>2<\/mn><\/msub><\/mrow>y_1=x_1+x_2<\/annotation><\/semantics><\/math>\u7684\u6362\u5143\uff0c\u548cy<\/mi>2<\/mn><\/msub>y_2<\/annotation><\/semantics><\/math>\u6ca1\u6709\u5173\u7cfb\uff0c\u53ef\u4ee5\u53d6\u4efb\u610f\u503c\uff0c\u5982\u679c\u53d6y<\/mi>2<\/mn><\/msub>=<\/mo>x<\/mi>2<\/mn><\/msub><\/mrow>y_2=x_2<\/annotation><\/semantics><\/math>\u3002\u5f97\u5230\u7684\u7ed3\u679c\u4e3a\uff1a f<\/mi>(<\/mo>x<\/mi>1<\/mn><\/msub>,<\/mo>x<\/mi>2<\/mn><\/msub>)<\/mo><\/mrow>=<\/mo>x<\/mi>1<\/mn>2<\/mn><\/msubsup>+<\/mo>x<\/mi>2<\/mn>2<\/mn><\/msubsup>+<\/mo>2<\/mn>x<\/mi>1<\/mn><\/msub>x<\/mi>2<\/mn><\/msub>=<\/mo>(<\/mo>x<\/mi>1<\/mn><\/msub>+<\/mo>x<\/mi>2<\/mn><\/msub>)<\/mo><\/mrow>2<\/mn><\/msup>=<\/mo>y<\/mi>1<\/mn>2<\/mn><\/msubsup><\/mrow>\nf(x_1,x_2)=x_1^2+x_2^2+2x_1x_2=(x_1+x_2)^2=y_1^2\n<\/annotation><\/semantics><\/math> \u53d6 A<\/mi>=<\/mo>(<\/mo>1<\/mn><\/mtd>1<\/mn><\/mtd><\/mtr>1<\/mn><\/mtd>1<\/mn><\/mtd><\/mtr><\/mtable>)<\/mo><\/mrow><\/mtd><\/mtr><\/mtable>\n\\begin{aligned}\nA=\\begin{pmatrix}\n1 & 1 \\\\\n1 & 1\n\\end{pmatrix}\n\\end{aligned}\n<\/annotation><\/semantics><\/math><\/p>\n

\u6b64\u65f6\u7684\u53d8\u6362\u5173\u7cfb\u4e3a\uff1a (<\/mo>y<\/mi>1<\/mn><\/msub><\/mtd><\/mtr>y<\/mi>2<\/mn><\/msub><\/mtd><\/mtr><\/mtable>)<\/mo><\/mrow>=<\/mo>(<\/mo>1<\/mn><\/mtd>1<\/mn><\/mtd><\/mtr>0<\/mn><\/mtd>1<\/mn><\/mtd><\/mtr><\/mtable>)<\/mo><\/mrow>(<\/mo>x<\/mi>1<\/mn><\/msub><\/mtd><\/mtr>x<\/mi>2<\/mn><\/msub><\/mtd><\/mtr><\/mtable>)<\/mo><\/mrow>=<\/mo>Q<\/mi>(<\/mo>x<\/mi>1<\/mn><\/msub><\/mtd><\/mtr>x<\/mi>2<\/mn><\/msub><\/mtd><\/mtr><\/mtable>)<\/mo><\/mrow><\/mrow>\n\\begin{pmatrix}y_1 \\\\ y_2\\end{pmatrix}=\\begin{pmatrix} 1 & 1 \\\\ 0 & 1\\end{pmatrix}\\begin{pmatrix}x_1 \\\\ x_2\\end{pmatrix}=Q\\begin{pmatrix}x_1 \\\\ x_2\\end{pmatrix}\n<\/annotation><\/semantics><\/math> \u90a3\u4e48\uff0c (<\/mo>x<\/mi>1<\/mn><\/msub><\/mtd><\/mtr>x<\/mi>2<\/mn><\/msub><\/mtd><\/mtr><\/mtable>)<\/mo><\/mrow><\/mtd>=<\/mo>Q<\/mi>\u2212<\/mo>1<\/mn><\/mrow><\/msup>(<\/mo>y<\/mi>1<\/mn><\/msub><\/mtd><\/mtr>y<\/mi>2<\/mn><\/msub><\/mtd><\/mtr><\/mtable>)<\/mo><\/mrow><\/mtd><\/mtr><\/mtd>=<\/mo>(<\/mo>1<\/mn><\/mtd>\u2212<\/mo>1<\/mn><\/mtd><\/mtr>0<\/mn><\/mtd>1<\/mn><\/mtd><\/mtr><\/mtable>)<\/mo><\/mrow>(<\/mo>y<\/mi>1<\/mn><\/msub><\/mtd><\/mtr>y<\/mi>2<\/mn><\/msub><\/mtd><\/mtr><\/mtable>)<\/mo><\/mrow><\/mtd><\/mtr>D<\/mi><\/mtd>=<\/mo>(<\/mo>1<\/mn><\/mtd>\u2212<\/mo>1<\/mn><\/mtd><\/mtr>0<\/mn><\/mtd>1<\/mn><\/mtd><\/mtr><\/mtable>)<\/mo><\/mrow><\/mtd><\/mtr><\/mtable>\n\\begin{aligned}\n\\begin{pmatrix}x_1 \\\\ x_2\\end{pmatrix}\n&=Q^{-1}\\begin{pmatrix}y_1 \\\\ y_2\\end{pmatrix} \\\\ \n&=\\begin{pmatrix} 1 & -1 \\\\ 0 & 1\\end{pmatrix}\\begin{pmatrix}y_1 \\\\ y_2\\end{pmatrix}\\\\\nD&=\\begin{pmatrix} 1 & -1 \\\\ 0 & 1\\end{pmatrix}\n\\end{aligned}\n<\/annotation><\/semantics><\/math> \u5373 {<\/mo>x<\/mi>1<\/mn><\/msub><\/mtd>=<\/mo>y<\/mi>1<\/mn><\/msub>\u2212<\/mo>y<\/mi>2<\/mn><\/msub><\/mtd><\/mtr>x<\/mi>2<\/mn><\/msub><\/mtd>=<\/mo>y<\/mi>2<\/mn><\/msub><\/mtd><\/mtr><\/mtable><\/mrow>\n\\left\\{\n\\begin{aligned}\nx_1&=y_1-y_2 \\\\\nx_2&=y_2\n\\end{aligned}\n\\right. \n<\/annotation><\/semantics><\/math> f<\/mi>(<\/mo>x<\/mi>)<\/mo><\/mrow><\/mtd>=<\/mo>x<\/mi>T<\/mi><\/msup>A<\/mi>x<\/mi>=<\/mo>(<\/mo>D<\/mi>y<\/mi>)<\/mo><\/mrow>T<\/mi><\/msup>A<\/mi>D<\/mi>y<\/mi>=<\/mo>y<\/mi>T<\/mi><\/msup>D<\/mi>T<\/mi><\/msup>A<\/mi>D<\/mi>y<\/mi><\/mtd><\/mtr><\/mtd>=<\/mo>y<\/mi>T<\/mi><\/msup>(<\/mo>1<\/mn><\/mtd>0<\/mn><\/mtd><\/mtr>\u2212<\/mo>1<\/mn><\/mtd>1<\/mn><\/mtd><\/mtr><\/mtable>)<\/mo><\/mrow>(<\/mo>1<\/mn><\/mtd>1<\/mn><\/mtd><\/mtr>1<\/mn><\/mtd>1<\/mn><\/mtd><\/mtr><\/mtable>)<\/mo><\/mrow>(<\/mo>1<\/mn><\/mtd>\u2212<\/mo>1<\/mn><\/mtd><\/mtr>0<\/mn><\/mtd>1<\/mn><\/mtd><\/mtr><\/mtable>)<\/mo><\/mrow>y<\/mi><\/mtd><\/mtr><\/mtd>=<\/mo>y<\/mi>1<\/mn>2<\/mn><\/msubsup><\/mtd><\/mtr><\/mtable>\n\\begin{aligned}\nf(x)&=x^TAx=(Dy)^TADy=y^TD^TADy\\\\\n&=y^T\\begin{pmatrix} 1 & 0 \\\\ -1 & 1\\end{pmatrix}\\begin{pmatrix}\n1 & 1 \\\\\n1 & 1\n\\end{pmatrix}\\begin{pmatrix} 1 & -1 \\\\ 0 & 1\\end{pmatrix}y \\\\\n&=y_1^2\n\\end{aligned}\n<\/annotation><\/semantics><\/math> \u663e\u7136\u6b64\u5904D<\/mi>T<\/mi><\/msup>\u2260<\/mo>D<\/mi>\u2212<\/mo>1<\/mn><\/mrow><\/msup><\/mrow>D^T \\neq D^{-1}<\/annotation><\/semantics><\/math>\uff0c\u867d\u7136\u53ef\u4ee5\u53d8\u6362\u6210\u4e86\u6807\u51c6\u5f62\uff0c\u4f46\u662f\u5e76\u4e0d\u662fd<\/mi>i<\/mi>a<\/mi>g<\/mi>(<\/mo>2<\/mn>,<\/mo>0<\/mn>)<\/mo><\/mrow><\/mrow>diag(2,0)<\/annotation><\/semantics><\/math>\u7684\u5f62\u5f0f\uff0cD<\/mi>D<\/annotation><\/semantics><\/math>\u4e5f\u4e0d\u662f\u7279\u5f81\u5411\u91cf\u77e9\u9635\u3002\u5e76\u4e14D<\/mi>D<\/annotation><\/semantics><\/math>\u4e0d\u662f\u6b63\u89c4\u77e9\u9635\uff0c\u4e0d\u80fd\u505a\u9149\u53d8\u6362\u3002D<\/mi>T<\/mi><\/msup>\u2260<\/mo>D<\/mi>\u2212<\/mo>1<\/mn><\/mrow><\/msup><\/mrow>D^T \\neq D^{-1}<\/annotation><\/semantics><\/math>\uff0c\u6b64\u53d8\u6362\u4e0d\u80fd\u548c\u7279\u5f81\u5411\u91cf\u548c\u7279\u5f81\u503c\u5efa\u7acb\u8054\u7cfb\u3002<\/p>\n

\u5982\u4f55\u7406\u89e3\u8fd9\u79cd\u53d8\u6362\u5462\uff1f<\/h4>\n

\u8fd9\u79cd\u53d8\u6362\u6548\u679c\u5982\u4e0b\u56fe\uff0c\u53d8\u6362\u540e\u7684\u5750\u6807\u8f74\u621045\u5ea6\u89d2\uff0c\u5e76\u4e14\u548cy<\/mi>2<\/mn><\/msub>y_2<\/annotation><\/semantics><\/math>\u65e0\u5173\u3002 \"\u4e0d\u53ef\u9006\u53d8\u6362\"<\/p>\n

\u5982\u679c\u77e9\u9635\u4e3aB<\/h3>\n

\u5176\u7279\u5f81\u503c\u4e3a\u91cd\u68391\uff0c\u4ec5\u5bf9\u5e94\u4e00\u4e2a\u7279\u5f81\u5411\u91cf\uff0c\u65e0\u6cd5\u5bf9\u89d2\u5316\u3002\u4f46\u662f\u4e8c\u6b21\u578b\u8fd8\u662f\u90a3\u4e2a\u5f0f\u5b50\uff0c\u4e3a\u4ec0\u4e48\u5374\u4e0d\u80fd\u5bf9\u89d2\u5316\u5462\uff1f \u4e8c\u6b21\u578b\u548c\u5bf9\u79f0\u77e9\u9635\u5177\u6709\u76f8\u540c\u7684\u8ba1\u7b97\u7279\u6027\uff0c\u8ba1\u7b97\u51fa\u6765\u7684\u7279\u5f81\u5411\u91cf\u6070\u597d\u548c\u6362\u5143\u53d8\u6362\u5173\u7cfb\u3002D<\/mi>T<\/mi><\/msup>D^T<\/annotation><\/semantics><\/math>\u8868\u793a\u6362\u5143\u53d8\u6362\u5173\u7cfb\uff0cD<\/mi>\u2212<\/mo>1<\/mn><\/mrow><\/msup>D^{-1}<\/annotation><\/semantics><\/math>\u8868\u793a\u7279\u5f81\u503c\u548c\u7279\u5f81\u5411\u91cf\u5173\u7cfb\uff0cD<\/mi>T<\/mi><\/msup>=<\/mo>D<\/mi>\u2212<\/mo>1<\/mn><\/mrow><\/msup><\/mrow>D^T=D^{-1}<\/annotation><\/semantics><\/math>\u5c06\u7279\u5f81\u503c\u7279\u5f81\u5411\u91cf\u5173\u7cfb\u548c\u6362\u5143\u5173\u7cfb\u8054\u7cfb\u4e86\u8d77\u6765\u3002<\/p>\n","protected":false},"excerpt":{"rendered":"

f(x)=a11x12+a22x22+\u22ef+annxn2+2a12x1x2+2a13x1x3+\u22ef+2an\u22121,n … <\/p>\n

\u7ee7\u7eed\u9605\u8bfb\u201c\u4e8c\u6b21\u578b\u4e0e\u77e9\u9635\u5bf9\u5e94\u5173\u7cfb\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-1616","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\/1616","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=1616"}],"version-history":[{"count":7,"href":"https:\/\/thereisno.top\/index.php?rest_route=\/wp\/v2\/posts\/1616\/revisions"}],"predecessor-version":[{"id":1663,"href":"https:\/\/thereisno.top\/index.php?rest_route=\/wp\/v2\/posts\/1616\/revisions\/1663"}],"wp:attachment":[{"href":"https:\/\/thereisno.top\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=1616"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/thereisno.top\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=1616"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/thereisno.top\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=1616"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}