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Eigenvalue proof

  1. Apr 9, 2009 #1
    1. The problem statement, all variables and given/known data
    Let λ be an eigenvalue of A. Then λ^2 is an eigenvalue of A^2




    3. The attempt at a solution

    I know I have to start by using the fact that λ is an e.v of A then set up an equation relating the eigenvalues and vectors to A which is: Ax=λx. And I understand that the equation for λ^2 and A^2 would be: A^2(x)=λ^2(x)...but i dont know how to prove that :-(
     
  2. jcsd
  3. Apr 9, 2009 #2
    Ax=λx,so AAX=Aλx=λAX=λ*λx,namely A^2(x)=λ^2(x)
     
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