r(A*A^T)=r(A^T*A)=r(A)
证明方程AX=0与A^TAX=0同解AX=0显然有A^T*AX=0A^T*AX=0则有X^T*A^T*AX=0即(AX)^T*AX=0,一个矩阵和它的转置相乘是0,则矩阵是0.则有AX=0同解说明基相同,基相同说明自由量数相等n-r(A^T*A)=n-r(A)则r(A^T*A)=r(A)这样证对吗?我看李永乐辅导讲义里有一道题用到了r(A^T*A)r(A)>=r(C)=r(AA^T)这样证明行吗?
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