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  • Unitary matrices

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  • Definition of unitary matrix
  • Unitary matrices are invertible.
  • Unitary matrices preserve orthogonal (orthonormal) bases.
  • Unitary matrices have orthogonal (orthonormal) rows/columns.
  • Unitary matrices preserve inner products.
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  1. Unitary matrices are invertible.

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  • Unitary matricesClose match
  • Definition of unitary matrixClose match
  • Unitary matrices have orthogonal (orthonormal) rows/columns.Close match
  • Unitary matrices preserve orthogonal (orthonormal) bases.Close match
  • Unitary matrices preserve inner products.Close match
  • InverseClose match
  • Elementary matrices are invertible/nonsingular.Close match
  • Definition of unit matrixClose match
  • A complex matrix is unitarily diagonalizable iff it is normalClose match
  • Normal matricesClose match
  • Hermitian matrices have real eigenvalues.Close match
  • The inverse of an invertible upper/lower triangular matrix is upper/lower triangular.Close match
  • Every complex square matrix is unitarily similar to an upper triangular matrixClose match
  • Hermitian matricesClose match
  • Equivalence theorem for nonsingular matrices: the transpose of the matrix A has an inverse.Close match
  • A nonsingular matrix can be written as a product of elementary matrices.Close match
  • Definition of normal matrixClose match
  • Triangular matricesClose match
  • Equivalence theorem for nonsingular matrices: the matrix A has an inverse.Close match
  • Equivalence theorem for nonsingular matrices: the determinant of A is nonzero.Close match

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