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Proving similar eigenvalues

  1. May 15, 2013 #1
    1. The problem statement, all variables and given/known data

    Let A and C be nxn matrices with C invertible. Prove that A and C-1AC have the same eigenvalues.


    2. Relevant equations

    B=C-1AC

    3. The attempt at a solution

    det(A-λI) =det(B-λI)
    det(A-λI) =det(C-1AC - λI)
    det(A-λI) =det(C-1AC - λC-1IC)
    det(A-λI) =det[CC-1(A-λI)] <<<< can you factor out a CC-1??
     
  2. jcsd
  3. May 15, 2013 #2

    Dick

    User Avatar
    Science Advisor
    Homework Helper

    You can't say C^(-1)AC=C^(-1)CA. The matrices A and C might not commute. Back up a step and think about it again.
     
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