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Math Help - Eigenvalues

  1. #1
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    Eigenvalues

    Just a quick question, given a matrix A and a diagonal matrix D

    Does DA(D^-1) always have the same eigenvalues as A?

    Thanks.
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  2. #2
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    Quote Originally Posted by Talamari View Post
    Just a quick question, given a matrix A and a diagonal matrix D

    Does DA(D^-1) always have the same eigenvalues as A?

    Thanks.

    Well, yes...but D doesn't even need to be diagonal: this is true for any invertible matrix D, since then A\,,\,DAD^{-1} are similar and thus they have the same characteristic polynomial.

    Tonio
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