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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 matrix-scalar product is the product of the adjoint and the conjugate.

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Definition of adjoint (conjugate transpose)Close match
The conjugate of a matrix-scalar product is the product of the conjugates.Close match
The adjoint of a product of matrices is the product of the adjoints in reverse order.Close match
Matrix adjoint is an involution.Close match
Transpose commutes with scalar multiplication.Close match
The conjugate of the transpose is the transpose of the conjugate.Close match
The conjugate of a product of matrices is the product of the conjugates.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
The adjoint of a sum is the sum of the adjoints.Close match
ConjugationClose match
Definition of conjugate of a matrixClose match
The inverse of a matrix can be expressed in terms of its matrix of cofactors.Close match
Definition of adjugate/classical adjoint of a matrixClose match
Definition of transpose of a matrixClose match
The transpose of a product of matrices is the product of the transposes in reverse order.Close match
The conjugate of the sum of matrices is the sum of the conjugates.Close match
Matrix transpose is an involution.Close match
Matrix transpose commutes with matrix inverse.Close match
The standard inner product on C^n can be written as the product of a vector and the adjoint of a vector.Close match

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