Cayley–Hamilton theorem是否可逆？
即是問以下的statement是否成立？
For a matrix polynomial equation p(A) = 0, the only matrices A can satisfy this matrix polynomial equation p(A) = 0 is that it exist some of its eigenvalue(s) λ satisfy this polynomial equation p(λ) = 0.
請詳細解釋。
Cayley–Hamilton theorem是否可逆？
2010-03-01 12:09 am
回答 (2)
2010-03-01 10:39 pm
✔ 最佳答案
If p(A)=0, t is any eigenvalue of A, then 0=p(A)v=p(t) v, so p(t)=0請問d大您問什麼問題?
2010-03-01 14:39:11 補充：
Let λ be an eigenvalue of A with eigenvector v (Av=λv), then p(A)v=p(λ)v.
While p(A)=0, so p(λ)v=0, p(λ)=0,
ie. eigenvalue(s) of A must be root(s) of p(x)=0.
For instance, if A satisfies matrix eq. X^2-4X+3I=0, then eigenvalue(s) of
A must be 1 or 3.
2010-03-01 7:59 am
應該是問
P( A ) = 0→P( λ )會不會等於0
P( A ) = 0→P( λ )會不會等於0
收錄日期: 2021-04-30 14:26:02
原文連結 [永久失效]:
https://hk.answers.yahoo.com/question/index?qid=20100228000010KK06642