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Math Help - Orthogonal diagonalization

  1. #1
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    Orthogonal diagonalization

    Would be grateful if anyone could help on this.

    Let Matrix A = 1 2 1
    2 4 2
    1 2 1

    Find orthogonal matrix P such that (P-1)AP is diagonal, where P-1 is P inverse?

    Thanks
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  2. #2
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    Quote Originally Posted by Jtown View Post
    Would be grateful if anyone could help on this.

    Let Matrix A = 1 2 1
    2 4 2
    1 2 1

    Find orthogonal matrix P such that (P-1)AP is diagonal, where P-1 is P inverse?

    Thanks
    Read this: http://www.fen.bilkent.edu.tr/~degt/math220/diag.pdf

    And this: Diagonalization

    And this: Diagonalization

    Now .... are you still stuck?
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  3. #3
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    Proof

    Thanks those sites were very helful. Understand that now.

    You wouldn't happen to know (or know of any sites) which show the proof that any eigenvalue of A is real, if A is a real symmetric matrix.
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