Hermitian Transpose
The Hermitian transpose is transposition then conjugation.
Contents
Description
The Hermitian transpose of a matrix A is calculated by transposing it and taking the complex conjugate.
There isn't a standard notation: use one of AH or A† ('dagger') or A*.
If AH = A-1, or if AAH = AHA = I, then A is unitary.
If AH = A, then A is Hermitian. This looks like a symmetric matrix where the complex components mirrored across the diagonal have flipped signs. Only a square matrix can be Hermitian.
Properties
The double transpose of a matrix is the original matrix: A** = A.
(A + B)* = A* + B*.
(AB)* = B*A*
(cA)* = c̅(A)*
The product of two unitary matrices is also unitary.