推 hunter0904:nilpotent A^n一定會是O 12/28 16:55
推 hunter0904:原因在於 入都是0 多項式會是(-x)^n = PA(x) 12/28 16:58
→ hunter0904:cayley-hamilton定理 PA(A)=O => A^n一定是O 12/28 16:59
※ 編輯: skill91002 來自: 140.117.120.229 (12/28 18:19)
1. Does it exist a (3*3) matrix A such that
4 [ 0 0 0 ] 9 [ 0 0 0 ]
A = [ 1 0 0 ] and A = [ 0 0 1 ] ?
[ 1 1 0 ] [ 0 1 1 ]
Justify your answer.
小黃的答案我看不懂耶
答案如下： 3
12 [ 4 ]
A = [ (A ) ] = 0
=> A : nilpotent
3
=> 3*3 的nilpotent A = 0
4
=> A = 0 矛盾
#
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