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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. Definition of orthogonally diagonalizable matrix

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  • A matrix is orthogonally diagonalizable if and only if it is symmetric.Close match
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  • An n-by-n matrix is diagonalizable if and only if it has n linearly independent eigenvectors.Close match
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  • An n-by-n matrix is diagonalizable if and only if the sum of the dimensions of the eigenspaces equals n.Close match
  • An n-by-n matrix is diagonalizable if and only if the union of the basis vectors for the eigenspaces is a basis for R^n (or C^n).Close match
  • Symmetric matricesClose match
  • A diagonalizable matrix is diagonalized by a matrix having the eigenvectors as columns.Close match
  • An n-by-n matrix with n distinct eigenvalues is diagonalizable.Close match
  • A complex matrix is unitarily diagonalizable iff it is normalClose match
  • Definition of symmetric matrixClose match
  • Definition of block diagonal matrixClose match
  • Normal matricesClose match
  • Definition of diagonalizable linear transformationClose match
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