1. PF Contest - Win "Conquering the Physics GRE" book! Click Here to Enter
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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

    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;
    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)
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook