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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 have orthogonal (orthonormal) rows/columns.

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  • Unitary matricesClose match
  • Definition of unitary matrixClose match
  • Unitary matrices preserve orthogonal (orthonormal) bases.Close match
  • Unitary matrices are invertible.Close match
  • Unitary matrices preserve inner products.Close match
  • A square real matrix has orthonormal columns iff its inverse is its transposeClose match
  • Normal matricesClose match
  • A complex matrix is unitarily diagonalizable iff it is normalClose match
  • A complex normal matrix has an orthonormal eigenvector basisClose match
  • Definition of unit matrixClose match
  • Every complex square matrix is unitarily similar to an upper triangular matrixClose match
  • Definition of normal matrixClose match
  • Definition of orthogonal matrixClose match
  • Definition of orthonormal set of vectorsClose match
  • Triangular matricesClose match
  • A matrix with real entries and orthonormal columns preserves norms.Close match
  • Orthogonality and projectionClose match
  • MatricesClose match
  • A matrix is orthogonally diagonalizable if and only if it is symmetric.Related
  • Distinct eigenvalues of a Hermitian matrix have orthogonal eigenvectors.Related

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