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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 an upper triangular matrix
  • Definition of a lower triangular matrix
  • The product of upper/lower triangular matrices is upper/lower triangular.
  • The inverse of an invertible upper/lower triangular matrix is upper/lower triangular.
  • Every complex square matrix is unitarily similar to an upper triangular matrix
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  1. Triangular matrices

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  • Definition of an upper triangular matrixClose match
  • Definition of a lower triangular matrixClose match
  • The product of upper/lower triangular matrices is upper/lower triangular.Close match
  • The inverse of an invertible upper/lower triangular matrix is upper/lower triangular.Close match
  • The determinant of a triangular matrix is the product of the entries on the diagonal.Close match
  • Every complex square matrix is unitarily similar to an upper triangular matrixClose match
  • Symmetric matricesClose match
  • The eigenvalues of a triangular matrix are the entries on the main diagonal.Close match
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  • The determinant of a matrix can be expressed as a product of the diagonal entries in a non-scaled echelon form.Close match
  • MatricesClose match
  • Particular types of matricesClose match
  • Factorization of matricesClose match
  • Normal matricesClose match
  • Matrix diagonalizationClose match
  • Definition of determinant of a matrix as a product of the diagonal entries in a non-scaled echelon form.Close match
  • Unitary matricesClose match
  • Block matricesClose match
  • Definition of square matrixClose match
  • Hermitian matricesClose match

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