\u8d85\u8fc7\u4e09\u7ef4\u4ee5\u4e0a\u7684\u65b9\u5dee\u5206\u5272\u5c5e\u4e8e\u591a\u7ef4\u65b9\u5dee\u5206\u5272\uff0c\u62c9\u683c\u6717\u65e5\u65b9\u6cd5\u4ecd\u7136\u9002\u7528\u4e8e\u9ad8\u7ef4\u7684\u60c5\u51b5\u3002<\/p>\n\n\n\n
\u6b64\u65f6\u53ef\u4ee5\u901a\u8fc7\u4e09\u7ef4\u65b9\u5dee\u5206\u5272\u7684\u89e3\u6cd5\u4e86\u89e3\u5230\u5176\u4e2d\u7684\u4e00\u4e9b\u60c5\u51b5\u3002\u5bf9\u4e8e\u62c9\u683c\u6717\u65e5\u65b9\u6cd5\u6240\u6784\u9020\u7684\\(L(a,b,c)\\)\u51fd\u6570\uff0c\u53ef\u4ee5\u5316\u7b80\u540e\u5f97\u5230\u5982\u4e0b\u65b9\u7a0b\u7ec4\uff1a<\/p>\n\n\n\n
\\[\\sum\\limits_{i = 1}^N {2(a{x_i} + b{y_i} + c{z_i}){x_i} + 2\\lambda a = 0} \\]<\/p>\n\n\n\n
\\[\\sum\\limits_{i = 1}^N {2(a{x_i} + b{y_i} + c{z_i}){y_i} + 2\\lambda b = 0} \\]<\/p>\n\n\n\n
\\[\\sum\\limits_{i = 1}^N {2(a{x_i} + b{y_i} + c{z_i}){z_i} + 2\\lambda c = 0} \\]<\/p>\n\n\n\n
\u5373\uff1a<\/p>\n\n\n\n
\\[ \\begin{array}{*{20}{c}}
{a({m_{xx}} + \\lambda ) + b{m_{xy}} + c{m_{xz}} = 0}\\\\
{a{m_{xy}} + b({m_{yy}} + \\lambda ) + c{m_{yz}} = 0}\\\\
{a{m_{xz}} + b{m_{yz}} + c({m_{zz}} + \\lambda ) = 0}
\\end{array} \\]<\/p>\n\n\n\n
\\[ \\left[ {\\begin{array}{*{20}{c}}
{m_{xx}}&{m_{xy}}&{m_{xz}}\\\\
{m_{xy}}&{m_{yy}}&{m_{yz}}\\\\
{m_{xz}}&{m_{yz}}&{m_{zz}}
\\end{array}} \\right] \\left[ {\\begin{array}{*{20}{c}}
a\\\\
b\\\\
c
\\end{array}} \\right] + \\lambda \\left[ {\\begin{array}{*{20}{c}} a\\\\ b\\\\ c \\end{array}} \\right] = 0\\]<\/p>\n\n\n\n
\u719f\u6089\u7ebf\u6027\u4ee3\u6570\u5f97\u8bfb\u8005\u53ef\u80fd\u5df2\u7ecf\u770b\u51fa\u4e86\u4e00\u4e9b\u4e1c\u897f\u3002\u8fd9\u4e2a\u65b9\u7a0b\u7ec4\u548c\u77e9\u9635\u7279\u5f81\u503c\u516c\u5f0f\\(A = |A – \\lambda E|= 0\\)\u57fa\u672c\u4e00\u81f4\u3002\\(\\lambda\\)\u662f\u7279\u5f81\u503c\uff0c\\(\\overrightarrow l = (a,b,c)\\)\u662f\u7279\u5f81\u5411\u91cf\uff08\u4e00\u6761\u76f4\u7ebf\u5b58\u5728\u4e24\u4e2a\u65b9\u5411\u63cf\u8ff0\uff0c\u521a\u597d\u7b26\u53f7\u76f8\u53cd\uff09\u3002<\/p>\n\n\n\n
\u4ee4\uff1a<\/p>\n\n\n\n
\\[\\begin{array}{*{20}{c}}
{\\overrightarrow X = ({x_1},{x_2},\u2026{x_n})}&{\\overrightarrow Y = ({y_1},{y_2},\u2026{y_n})}&{\\overrightarrow Z = ({z_1},{z_2},\u2026{z_n})}
\\end{array}\\]<\/p>\n\n\n\n
\u5219\uff1a<\/p>\n\n\n\n
\\[ A = \\left[ {\\begin{array}{*{20}{c}}
{m_{xx}}&{m_{xy}}&{m_{xz}}\\\\
{m_{xy}}&{m_{yy}}&{m_{yz}}\\\\
{m_{xz}}&{m_{yz}}&{m_{zz}}
\\end{array}} \\right] \\\\ = \\left[ {\\begin{array}{*{20}{c}}
{\\overrightarrow X \\cdot \\overrightarrow X}&{\\overrightarrow X \\cdot \\overrightarrow Y}&{\\overrightarrow X \\cdot \\overrightarrow Z}\\\\
{\\overrightarrow Y \\cdot \\overrightarrow X}&{\\overrightarrow Y \\cdot \\overrightarrow Y}&{\\overrightarrow Y \\cdot \\overrightarrow Z}\\\\
{\\overrightarrow Z \\cdot \\overrightarrow X}&{\\overrightarrow Z \\cdot \\overrightarrow Y}&{\\overrightarrow Z \\cdot \\overrightarrow Z}
\\end{array}} \\right] \\\\ = \\left[ {\\begin{array}{*{20}{c}} {\\overrightarrow X }\\\\ {\\overrightarrow Y }\\\\ {\\overrightarrow Z } \\end{array}} \\right] \\times \\left[ {\\begin{array}{{20}{c}} {\\overrightarrow X }&{\\overrightarrow Y }&{\\overrightarrow Z } \\end{array}} \\right] \\]<\/p>\n\n\n\n
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