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  • Triangular 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. Every complex square matrix is unitarily similar to an upper triangular matrix

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  • Every square matrix is similar to one in Jordan form.Close match
  • Triangular matricesClose match
  • Definition of Schur triangulationClose match
  • A complex matrix is unitarily diagonalizable iff it is normalClose match
  • Every matrix has an eigenvalue over the complex numbers.Close match
  • The product of upper/lower triangular matrices is upper/lower triangular.Close match
  • Matrix diagonalizationClose match
  • The inverse of an invertible upper/lower triangular matrix is upper/lower triangular.Close match
  • Definition of similar matricesClose match
  • Hermitian matricesClose match
  • Unitary matricesClose match
  • Similar matrices have the same eigenvalues and the same characteristic polynomials.Close match
  • Similarity of matrices is an equivalence relationClose match
  • Unitary matrices have orthogonal (orthonormal) rows/columns.Close match
  • The eigenvalues of a triangular matrix are the entries on the main diagonal.Close match
  • Normal matricesClose match
  • Unitary matrices preserve orthogonal (orthonormal) bases.Close match
  • Definition of an upper triangular matrixClose match
  • Symmetric matricesClose match
  • A matrix is orthogonally diagonalizable if and only if it is symmetric.Close match

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