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  • Hermitian matrices

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  • Definition of Hermitian/self-adjoint matrix
  • Multiplication by a Hermitian matrix commutes with the standard inner product on C^n.
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  1. Multiplication by a Hermitian matrix commutes with the standard inner product on C^n.

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  • Hermitian matricesClose match
  • Definition of Hermitian/self-adjoint matrixClose match
  • Hermitian matrices have real eigenvalues.Close match
  • A matrix turns into its adjoint when moved to the other side of the standard inner product on C^n.Close match
  • Transpose and adjointClose match
  • Normal matricesClose match
  • Distinct eigenvalues of a Hermitian matrix have orthogonal eigenvectors.Close match
  • Definition of normal matrixClose match
  • Scalar multiplicationClose match
  • MultiplicationClose match
  • Unitary matricesClose match
  • Every complex square matrix is unitarily similar to an upper triangular matrixClose match
  • Symmetric matricesClose match
  • The conjugate of vector-scalar multiplication in C^n is the product of the conjugates.Close match
  • Operations on matricesRelated
  • ConjugationRelated
  • A matrix with real entries has eigenvalues occurring in conjugate pairs.Related
  • A complex matrix is unitarily diagonalizable iff it is normalRelated
  • Unitary matrices preserve inner products.Related
  • Complex inner products conjugate scalars in the first argumentRelated

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