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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 preserve orthogonal (orthonormal) bases.

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  • Unitary matrices have orthogonal (orthonormal) rows/columns.Close match
  • Unitary matrices preserve inner products.Close match
  • Unitary matricesClose match
  • Definition of unitary matrixClose match
  • Unitary matrices are invertible.Close match
  • A complex normal matrix has an orthonormal eigenvector basisClose match
  • Definition of orthonormal basis of a (sub)spaceClose match
  • A complex matrix is unitarily diagonalizable iff it is normalClose match
  • Normal matricesClose match
  • A matrix is orthogonally diagonalizable if and only if it is symmetric.Close match
  • Every complex square matrix is unitarily similar to an upper triangular matrixClose match
  • Distinct eigenvalues of a Hermitian matrix have orthogonal eigenvectors.Close match
  • Orthogonality and projectionClose match
  • Eigenvectors of a symmetric matrix with different eigenvalues are orthogonal.Close match
  • Definition of orthogonal matrixClose match
  • The spectral theorem for symmetric matricesClose match
  • A matrix with real entries and orthonormal columns preserves norms.Close match
  • Equivalence theorem for nonsingular matrices: the matrix A is a change-of-basis matrix.Close match
  • Definition of orthogonally diagonalizable matrixClose match
  • Equivalence theorem for nonsingular matrices: the rows of A are a basis for R^n (or C^n).Close match

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