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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.
  • Definition of orthogonally diagonalizable matrix
  • A matrix is orthogonally diagonalizable if and only if it is symmetric.
  • The spectral theorem for symmetric matrices
  • Formula for the spectral decomposition for a symmetric matrix
  • Definition of skew-symmetric matrix
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  1. Formula for the spectral decomposition for a symmetric matrix

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  • The spectral theorem for symmetric matricesClose match
  • Symmetric matricesClose match
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  • Eigenvectors of a symmetric matrix with different eigenvalues are orthogonal.Close match
  • A matrix is orthogonally diagonalizable if and only if it is symmetric.Close match
  • A complex normal matrix has an orthonormal eigenvector basisClose match
  • Definition of singular value decomposition (SVD)Related
  • Definition of symmetric matrixRelated
  • Matrix diagonalizationRelated
  • Factorization of matricesRelated
  • Symmetric matrices are square.Related
  • Normal matricesRelated
  • Formula for computing the least squares solution to a linear system.Related
  • Formula for computing the least squares solution to a linear systemRelated
  • Definition of skew-symmetric matrixRelated
  • Definition of Cholesky decompositionRelated
  • Distinct eigenvalues of a Hermitian matrix have orthogonal eigenvectors.Related
  • Every complex square matrix is unitarily similar to an upper triangular matrixRelated
  • Eigenvalues and operations on matricesRelated
  • Eigenvectors with distinct eigenvalues are linearly independent.Related

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