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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. Eigenvectors of a symmetric matrix with different eigenvalues are orthogonal.

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  • Distinct eigenvalues of a Hermitian matrix have orthogonal eigenvectors.Close match
  • Eigenvectors with distinct eigenvalues are linearly independent.Close match
  • The spectral theorem for symmetric matricesClose match
  • A matrix is orthogonally diagonalizable if and only if it is symmetric.Close match
  • Hermitian matrices have real eigenvalues.Close match
  • Symmetric matricesClose match
  • A matrix with real entries has eigenvalues occurring in conjugate pairs.Close match
  • Definition of eigenvector of a matrixClose match
  • Eigenvalues and eigenvectorsClose match
  • Unitary matrices preserve orthogonal (orthonormal) bases.Close match
  • Equivalence theorem for nonsingular matrices: the matrix A does not have 0 as an eigenvalue.Close match
  • Every matrix has an eigenvalue over the complex numbers.Close match
  • Definition of orthogonally diagonalizable matrixClose match
  • Definition of orthogonal matrixClose match
  • Eigenvalues and operations on matricesClose match
  • Definition of eigenvalue of a matrixClose match
  • Formula for the spectral decomposition for a symmetric matrixClose match
  • Every complex square matrix is unitarily similar to an upper triangular matrixClose match
  • Definition of skew-symmetric matrixClose match
  • A complex normal matrix has an orthonormal eigenvector basisRelated

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