Hermitian

The hermitian of a matrix is defined as the complex conjugate transpose which modifies the matrix by:

• transposing the matrix
• conjugating all complex numbers \begin{bmatrix} 1 & 1+2i \\ 1-5i & 9 \end{bmatrix}^H \= \begin{bmatrix} 1 & 1+5i \\ 1-2i & 9 \end{bmatrix} The hermitian of a real matrix has no effect since for any $a\in \mathrm{Re}$, $a+i0$ and therefore $a^H=a$