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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 inner products.

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  • Unitary matrices preserve orthogonal (orthonormal) bases.Close match
  • Unitary matricesClose match
  • Unitary matrices have orthogonal (orthonormal) rows/columns.Close match
  • Definition of unitary matrixClose match
  • Unitary matrices are invertible.Close match
  • A matrix with real entries and orthonormal columns preserves dot products.Close match
  • A matrix with real entries and orthonormal columns preserves norms.Close match
  • Inner productsClose match
  • Inner products in coordinate spacesClose match
  • Normal matricesClose match
  • The standard inner product on R^n is commutative.Close match
  • The complex inner product is conjugate symmetricClose match
  • A complex matrix is unitarily diagonalizable iff it is normalRelated
  • A complex normal matrix has an orthonormal eigenvector basisRelated
  • Complex inner products conjugate scalars in the first argumentRelated
  • Orthogonality and projectionRelated
  • Multiplication by a Hermitian matrix commutes with the standard inner product on C^n.Related
  • A matrix turns into its adjoint when moved to the other side of the standard inner product on C^n.Related
  • Hermitian matricesRelated
  • Definition of unit matrixRelated

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