Definition:Hermitian Conjugate

Definition
Let $\mathbf A = \left[{\alpha}\right]_{m n}$ be an $m \times n$ matrix.

Then the Hermitian conjugate of $\mathbf A$ is denoted $\mathbf A^\dagger$ and is defined as:


 * $\mathbf A^\dagger = \left[{\beta}\right]_{n m}: \forall i \in \left[{1 \,.\,.\, n}\right], j \in \left[{1 \,.\,.\, m}\right]: \beta_{i j} = \overline \alpha_{j i}$

Also denoted as
The Hermitian conjugate of a matrix $\mathbf A$ is also denoted by $\mathbf A^*$ or $\mathbf A^{\mathrm H}$.

Also known as
The Hermitian conjugate is also known as the Hermitian transpose, conjugate transpose or adjoint matrix.

Also see

 * Definition:Adjoint Operator