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  • Conjugation

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  • Definition of conjugate of a matrix
  • Matrix conjugation is an involution.
  • The conjugate of the sum of matrices is the sum of the conjugates.
  • The conjugate of a matrix-scalar product is the product of the conjugates.
  • The conjugate of a product of matrices is the product of the conjugates.
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  1. Matrix conjugation is an involution.

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  • Definition of conjugate of a matrixClose match
  • ConjugationClose match
  • The conjugate of the sum of matrices is the sum of the conjugates.Close match
  • The conjugate of a matrix-scalar product is the product of the conjugates.Close match
  • Matrix adjoint is an involution.Close match
  • Matrix inverse is an involution.Close match
  • The conjugate of a product of matrices is the product of the conjugates.Close match
  • Matrix transpose commutes with matrix inverse.Close match
  • Matrix transpose is an involution.Close match
  • The conjugate of the transpose is the transpose of the conjugate.Close match
  • Matrix multiplication is associative.Close match
  • Matrix-scalar multiplication is commutativeClose match
  • Matrix addition is commutative and associative.Close match
  • Transpose and adjointClose match
  • Matrix cancellation requires an invertibility or rank hypothesisClose match
  • The complex inner product is conjugate symmetricClose match
  • Complex inner products conjugate scalars in the first argumentClose match
  • Hermitian matricesClose match
  • Matrix multiplication is not commutative in general.Close match
  • Matrix-vector product is associativeClose match

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