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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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The adjoint of a product of matrices is the product of the adjoints in reverse order.

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