叉乘反对称矩阵 什么是矩阵的叉乘？
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a1 a2 a3
b1 b2 b3
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\u516c\u5f0f\uff1a|c|=|a\u00d7b|=|a||b|sin\u3002
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\u4e3e\u4f8b\uff1aa=[1,2,3],b=[4,5,6]\uff0c\u5219cross(a,b)=[-3 6 -3]\u3002\u5b83\u8868\u793a\u7684\u610f\u601d\u662f\u4e09\u7ef4\u7a7a\u95f4\u4e2d\u7684\u4e24\u4e2a\u70b9A(1,2,3)\u548cB(4,5,6),\u518d\u52a0\u4e0a\u539f\u70b9O\uff0c\u5219\u6784\u6210\u7684\u4e24\u4e2a\u5411\u91cfOA\uff0cOB\uff0c\u5219cross(a,b)\u5c31\u662f\u5782\u76f4\u5e73\u9762OAB\u7684\u5411\u91cf\uff0c\u5b83\u7684\u6a21\u662f\u4e09\u89d2\u5f62OAB\u9762\u79ef\u76842\u500d\u3002
\u6269\u5c55\u8d44\u6599\uff1a
\u77e9\u9635\u5f62\u5f0f
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i\u00d7j=k\uff1b
j\u00d7k=i\uff1b
k\u00d7i=j\uff1b
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a=[a1\uff0ca2\uff0ca3]=a1i+a2j+a3k\uff1b
b=[b1\uff0cb2\uff0cb3]=b1i+b2j+b3k\uff1b
\u5219a\u00d7b=[a2b3-a3b2\uff0ca3b1-a1b3\uff0ca1b2-a2b1]\u3002
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\u53c2\u8003\u8d44\u6599\u6765\u6e90\uff1a\u767e\u5ea6\u767e\u79d1--\u5411\u91cf\u79ef
\u53c2\u8003\u8d44\u6599\u6765\u6e90\uff1a\u767e\u5ea6\u767e\u79d1--\u77e9\u9635
设向量u=[x2, y2, z2].', 则向量v和向量u的叉积v×u可转换为反对陈矩阵A与向量u的乘积,
即cross(v,u)和A*u结果一致.
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