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  • Transpose and adjoint

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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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