作者iyenn (晓风)
看板Grad-ProbAsk
标题Re: [理工] [线代]-Jordan form
时间Fri Nov 13 23:13:46 2009
※ 引述《gn00618777 (123)》之铭言：
: 请教一下
: if a matrix A has the property that A^k=0 for some postive integer
: show A-I is invertible？
let Ax=qx
q is eigenvalue of A
and x is corresponding eigenvector
A^kx=q^kx=0
x=/=0 , s.t. q^k=0
=>q=0
all eigenvalue is equal to zero.
s.t. A-I have nonzero eingenvalue
and det(A-I)=/=0
->A-I is invertible
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1F：推 gn00618777:多谢！ 11/13 23:49