Hermitian Conjugate

We call the matrix with complex elements as complex matrix. Similar to matrix transpose, we can define a Hermitian conjugate operation, that is, transpose a matrix and then take complex conjugation for each matrix element

$$A_{ij}^{†}=A_{ji}^{\ast }=\overline{A_{ji}}$$

(for any $c\in \mathbb{C}$, $c^{\ast }$ or $\bar{c}$ stand for the conjugation of $c$)

Note that when the matrix elements are all real, the Hermitian conjugation is consistent to matrix transpose. 

$A^{†}$ Also known as the adjoint matrix (do not confuse it with adjugate matrix)