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  • Operations on matrices

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  • Addition
  • Conjugation
  • Scalar multiplication
  • Row operations
  • Matrix-vector products
  • Multiplication
  • Transpose and adjoint
  • Inverse

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  • Definition of transpose of a matrix
  • Matrix transpose is an involution.
  • The conjugate of the transpose is the transpose of the conjugate.
  • Definition of adjoint (conjugate transpose)
  • The adjoint of a sum is the sum of the adjoints.
  • The adjoint of a matrix-scalar product is the product of the adjoint and the conjugate.
  • Matrix adjoint is an involution.
  • The transpose of a sum of matrices is the sum of the transposes.
  • Transpose commutes with scalar multiplication.
  • The transpose of a product of matrices is the product of the transposes in reverse order.
  • The adjoint of a product of matrices is the product of the adjoints in reverse order.
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  1. Transpose and adjoint

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  • Definition of transpose of a matrixClose match
  • Matrix adjoint is an involution.Close match
  • Matrix transpose is an involution.Close match
  • Definition of adjoint (conjugate transpose)Close match
  • The adjoint of a product of matrices is the product of the adjoints in reverse order.Close match
  • The conjugate of the transpose is the transpose of the conjugate.Close match
  • The transpose of a sum of matrices is the sum of the transposes.Close match
  • ConjugationClose match
  • Operations on matricesClose match
  • The transpose of a product of matrices is the product of the transposes in reverse order.Close match
  • Transpose commutes with scalar multiplication.Close match
  • The adjoint of a matrix-scalar product is the product of the adjoint and the conjugate.Close match
  • A matrix turns into its adjoint when moved to the other side of the standard inner product on C^n.Close match
  • The adjoint of a sum is the sum of the adjoints.Close match
  • InverseClose match
  • MultiplicationClose match
  • Hermitian matricesClose match
  • Matrix-vector productsClose match
  • AdditionClose match
  • Definition of conjugate of a matrixClose match

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