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Homework Help: Eigenvalue Problem

  1. Sep 12, 2010 #1
    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. jcsd
  3. Sep 12, 2010 #2
    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)
     
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