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Symmetric matrices
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Definition of symmetric matrix
Symmetric matrices are square.
Eigenvectors of a symmetric matrix with different eigenvalues are orthogonal.
The spectral theorem for symmetric matrices
Formula for the spectral decomposition for a symmetric matrix
Definition of orthogonally diagonalizable matrix
A matrix is orthogonally diagonalizable if and only if it is symmetric.
Definition of skew-symmetric matrix
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A matrix is orthogonally diagonalizable if and only if it is symmetric.
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Symmetric matrices