# Homework Help: Eigenvalue Problem

1. Sep 12, 2010

### Lanthanum

1. The problem statement, all variables and given/known data
Given that q is an eigenvalue of a square matrix A with corresponding eigenvector x, show that qk is an eigenvalue of Ak and x is a corresponding eigenvector.

2. Relevant equations
N/A

3. The attempt at a solution
I really haven't been able to get far, but;

If x is an eigenvector of A corresponding to q, then;
0=(A-qI)x
To complete the proof I need to use this equation to show that (Ak-qkI)x=0, and this is where I'm having trouble.
If anyone has time to help I would really appreciate it.

2. Sep 12, 2010

### hgfalling

I think you might want to use a different definition of an eigenvalue. Then the proof is really easy, with like hardly any algebra at all.
(edit: well, rearrange the one you have, I guess)