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Prove or disprove: A and A transpose have the same eigenspaces

  1. Feb 19, 2010 #1
    1. The problem statement, all variables and given/known data

    Prove or disprove: A and AT have the same eigenspaces.

    2. Relevant equations



    3. The attempt at a solution

    I know that A and AT have the same determinant and so they have the same characteristic polynomial and eigenvalues, but then if they are transposed then the stuff above and below the main diagonal is swapped then they wouldn't have the same eigenspaces? Unless they were symmetric?
     
  2. jcsd
  3. Feb 19, 2010 #2

    Dick

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    If you don't think it's true, try and create a simple example to show it isn't true. That would be a disproof.
     
  4. Feb 19, 2010 #3
    Okay so I did that and showed that its not true.. unless it was symmetric. Does that count as a disprove?
     
  5. Feb 19, 2010 #4
    No, you will need to come up with a specific counterexample if you want to disprove it.
     
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