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Math Help - Quick Facts on Orthogonal Matrices

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    Quick Facts on Orthogonal Matrices

    Trying to verify some stuff for orthogonal matrices by making some factual statements. If I'm wrong, could I get some help or if someone could just say yes/no/right/wrong?

    ---> an orthogonal matrix doesn't guarantee that it is orthogonally diagonalizable. (I think... not sure)

    ---> The dimension of an eigenspace of a symmetric matrix equals the muiltiplicity of the corresponding eigenvalue.
    Last edited by crystal-maiden; February 1st 2009 at 10:34 AM.
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    Quote Originally Posted by crystal-maiden View Post
    Trying to verify some stuff for orthogonal matrices by making some factual statements. If I'm wrong, could I get some help or if someone could just say yes/no/right/wrong?

    ---> an orthogonal matrix doesn't guarantee that it is orthogonally diagonalizable. (I think... not sure)

    ---> The dimension of an eigenspace of a symmetric matrix equals the muiltiplicity of the corresponding eigenvalue.
    1) False. It is normal, so it is orthogonally diagble.

    2) True. A symmetric matrix is diagonalizable, thus it is non-defective and thus geometric multiplicity = alg. multiplicity
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