Re: [理工] [線代]-Jordan form

[iyenn (曉風)]

※ 引述《gn00618777 (123)》之銘言：
: 請教一下
: 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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