Definition:Hermitian Conjugate

Definition
Let $\mathbf A = \sqbrk \alpha_{m n}$ be an $m \times n$ matrix over the complex numbers $\C$.

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


 * $\mathbf A^\dagger = \sqbrk \beta_{n m}: \forall i \in \set {1, 2, \ldots, n}, j \in \set {1, 2, \ldots, m}: \beta_{i j} = \overline {\alpha_{j i} }$

where $\overline {\alpha_{j i} }$ denotes the complex conjugate of $\alpha_{j i}$.

That is, it is the transpose of the complex conjugate of $\mathbf A$.

Also see

 * Definition:Adjoint Operator