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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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