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  • Particular types of matrices

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  • Echelon matrices
  • Definition of unit matrix
  • Definition of permutation matrix
  • Elementary matrices
  • Triangular matrices
  • Block matrices
  • Symmetric matrices
  • Nilpotent matrices
  • Definition of orthogonal matrix
  • Unitary matrices
  • Definition of band matrix
  • Definition of Vandermonde matrix
  • Definition of Markov matrix
  • Hermitian matrices
  • Normal matrices
  • A matrix with real entries has eigenvalues occurring in conjugate pairs.
  • Hermitian matrices have real eigenvalues.
  • Distinct eigenvalues of a Hermitian matrix have orthogonal eigenvectors.
  • Definition of positive-definite matrix
  • Formula for the determinant of a 2-by-2 matrix.
  • Formula for the determinant of a 3-by-3 matrix.
  • The determinant of a triangular matrix is the product of the entries on the diagonal.
  • The eigenvalues of a triangular matrix are the entries on the main diagonal.
  • Theorem describing the determinants of elementary 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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  1. Symmetric matrices

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