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Homework Help: Similar matrices

  1. Apr 27, 2014 #1
    1. The problem statement, all variables and given/known data
    A=[a,1;0,a] B=[a,0;0,a]
    If I want to show if matrix A is NOT similar to matrix B. Is it enough to show that B=/=Inv(P)*A*P? Or would I need to show that they do not have both the same eigenvalues and corresponding eigenvectors?
  2. jcsd
  3. Apr 27, 2014 #2


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    It would be enough to show B=/=Inv(P)*A*P for any invertible matrix P, if you have a clever way to do that. But I think the eigenvalue/eigenvector approach is more straightforward. If you calculate those for each matrix what do you get?
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