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Math Help - Eigenvalues and Matrices

  1. #1
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    Eigenvalues and Matrices

    Hi

    Just after a bit of pointing in the right direction. I have 3 eigenvalues and I am trying to find the matrix that they correspond to.

    How do I do it? It is really stumping me!!

    Thanks very much
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  2. #2
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    Are you trying to find the eigenvectors? Or are you trying to find the original matrix A from its eigenvalues?
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  3. #3
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    The original matrix A
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  4. #4
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    Well, I'm afraid you're not going to be able to determine the matrix A uniquely. There are, in general, infinitely many matrices that are similar to A that have the same eigenvalues. Do you know the size of A?
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  5. #5
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    I believe the matrix size is 3x3
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  6. #6
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    In that case, assuming you have three distinct eigenvalues, the best you can do is construct a diagonal matrix similar to A. That is, you can construct a diagonal matrix D such that there exists an invertible matrix P such that A=PDP^{-1}. You construct D by simply having your 3 eigenvalues on the main diagonal, and zeros everywhere else.

    If you have more conditions on A, you might be able to say more than this.
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  7. #7
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    I will give that a go and see how I get on - Cheers
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  8. #8
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    Right-ho.
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  9. #9
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    It worked - I got the answer I should have - thanks again!!
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  10. #10
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    You're very welcome. Have a good one!
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