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Thread: [Linear Algebra] Orthogonal Eigenbases

  1. #1
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    [Linear Algebra] Orthogonal Eigenbases

    If I am given a matrix, and told to determine if it has an orthogonal eigenbasis, is it enough to say yay/nay base on if it is symmetric or not?
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    Re: [Linear Algebra] Orthogonal Eigenbases

    I guess I should ask the question differently...

    A matrix can have an orthogonal eigenbasis if it is not symmetrical. But are symmetrical matrices guaranteed to have a orthogonal eigenbasis?
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  3. #3
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    Re: [Linear Algebra] Orthogonal Eigenbases

    Quote Originally Posted by MrJank View Post
    I guess I should ask the question differently...

    A matrix can have an orthogonal eigenbasis if it is not symmetrical. But are symmetrical matrices guaranteed to have a orthogonal eigenbasis?
    real symmetric matrices are guaranteed to have an orthogonal eigenbasis.
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