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Math Help - Properties of real symmetric matrices

  1. #1
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    Properties of real symmetric matrices

    Hello Everyone, what are properties of real symmetric nxn matrices other than
    (1) A \in M_{n \times \n}\Rightarrow A = A^t
    (2) \text{dim}M_{n\times n} = \frac{n(n+1)}{2}

    I can't think of any others...
    A little help would be appreciated
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  2. #2
    A Plied Mathematician
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    The eigenvalues are real, and the eigenvectors are an orthonormal basis. In fact, it is diagonalizable.
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