矩阵的左邻空间怎么求

\u6c42\u6559\u4ec0\u4e48\u662f\u77e9\u9635\u7684\u5217\u7a7a\u95f4\uff0c\u5982\u4f55\u6c42\u3002

\u77e9\u9635A\u7684\u96f6\u7a7a\u95f4\u662f\u6307\u65b9\u7a0b\u7ec4AX=0\u7684\u89e3\u5411\u91cf\u6784\u6210\u7684\u7a7a\u95f4\uff0c\u4e5f\u5c31\u662fAX=0\u7684\u89e3\u7a7a\u95f4\u3002
\u77e9\u9635\u7684\u5217\u7a7a\u95f4\u662f\u6307\u77e9\u9635\u7684\u5217\u5411\u91cf\u7ec4\u6784\u6210\u7684\u7a7a\u95f4\uff0c\u4e5f\u5c31\u662f\u5c06\u5217\u5411\u91cf\u7ec4\u7684\u6781\u5927\u7ebf\u6027\u65e0\u5173\u7ec4\u627e\u51fa\u6765\uff0c\u7136\u540e\u505a\u7ebf\u6027\u7ec4\u5408\u800c\u751f\u6210\u7684\u6240\u6709\u5411\u91cf\u6784\u6210\u7684\u7a7a\u95f4\u3002
\u5047\u5982\u8bf4a1,a2,a3\u751f\u6210\u7684\u7a7a\u95f4\uff0c\u5c31\u662fa1,a2,a3\u4efb\u610f\u7ebf\u6027\u7ec4\u6210\u6784\u6210\u7684\u7a7a\u95f4\u3002

\u6269\u5c55\u8d44\u6599\uff1a
\u77e9\u9635\u5728\u7269\u7406\u5b66\u4e2d\u7684\u53e6\u4e00\u7c7b\u6cdb\u5e94\u7528\u662f\u63cf\u8ff0\u7ebf\u6027\u8026\u5408\u8c03\u548c\u7cfb\u7edf\u3002\u8fd9\u7c7b\u7cfb\u7edf\u7684\u8fd0\u52a8\u65b9\u7a0b\u53ef\u4ee5\u7528\u77e9\u9635\u7684\u5f62\u5f0f\u6765\u8868\u793a\uff0c\u5373\u7528\u4e00\u4e2a\u8d28\u91cf\u77e9\u9635\u4e58\u4ee5\u4e00\u4e2a\u5e7f\u4e49\u901f\u5ea6\u6765\u7ed9\u51fa\u8fd0\u52a8\u9879\uff0c\u7528\u529b\u77e9\u9635\u4e58\u4ee5\u4f4d\u79fb\u5411\u91cf\u6765\u523b\u753b\u76f8\u4e92\u4f5c\u7528\u3002\u6c42\u7cfb\u7edf\u7684\u89e3\u7684\u6700\u4f18\u65b9\u6cd5\u662f\u5c06\u77e9\u9635\u7684\u7279\u5f81\u5411\u91cf\u6c42\u51fa\uff08\u901a\u8fc7\u5bf9\u89d2\u5316\u7b49\u65b9\u5f0f\uff09\uff0c\u79f0\u4e3a\u7cfb\u7edf\u7684\u7b80\u6b63\u6a21\u5f0f\u3002
\u53c2\u8003\u8d44\u6599\u6765\u6e90\uff1a\u767e\u5ea6\u767e\u79d1-\u77e9\u9635

\u6218\u7565\u5730\u4f4d\u4e0e\u884c\u52a8\u8bc4\u4ef7\u77e9\u9635(SPACE\u77e9\u9635) \u6218\u7565\u5730\u4f4d\u4e0e\u884c\u52a8\u8bc4\u4ef7\u77e9\u9635\uff08Strategic Position and Action Evaluation Matrix\uff0c\u7b80\u79f0SPACE\u77e9\u9635\uff09 \u4e3b\u8981\u662f\u5206\u6790\u4f01\u4e1a\u5916\u90e8\u73af\u5883\u53ca\u4f01\u4e1a\u5e94\u8be5\u91c7\u7528\u7684\u6218\u7565\u7ec4\u5408\u3002 SPACE\u77e9\u9635\u6709\u56db\u4e2a\u8c61\u9650\u5206\u522b\u8868\u793a\u4f01\u4e1a\u91c7\u53d6\u7684\u8fdb\u53d6\u3001\u4fdd\u5b88\u3001 \u9632\u5fa1\u548c\u7ade\u4e89\u56db\u79cd\u6218\u7565\u6a21\u5f0f\u3002 \u8fd9\u4e2a\u77e9\u9635\u7684\u4e24\u4e2a\u6570\u8f74\u5206\u522b\u4ee3\u8868\u4e86\u4f01\u4e1a\u7684\u4e24\u4e2a\u5185\u90e8\u56e0\u7d20\u2014\u2014\u8d22\u52a1\u4f18\u52bf\uff08 FS\uff09\u548c\u7ade\u4e89\u4f18\u52bf\uff08CA\uff09\uff1b\u4e24\u4e2a\u5916\u90e8\u56e0\u7d20\u2014\u2014\u73af\u5883\u7a33\u5b9a\u6027\uff08ES\uff09 \u548c\u4ea7\u4e1a\u4f18\u52bf\uff08IS\uff09\u3002 \u8fd9\u56db\u4e2a\u56e0\u7d20\u5bf9\u4e8e\u4f01\u4e1a\u7684\u603b\u4f53\u6218\u7565\u5730\u4f4d\u662f\u6700\u4e3a\u91cd\u8981\u7684

\u6ee1\u610f\u8bf7\u91c7\u7eb3

零空间就是求Ax=0的解

A化成最简型:
1 0 2 0 1
0 1 3 0 0
0 0 0 1 4

所以Ax=0的解是:
[x1,x2,x3,x4,x5]' = x3[-2 -3 1 0 0]' + x5[-1 0 0 -4 1]'

所以零空间为这两个向量张成的空间:
span([-2 -3 1 0 0]',[-1 0 0 -4 1]')

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