Find the hermetian conjugates of the following matrices. Which of these is hermetian?
$A = \begin{bmatrix} 1 + i & 4-7i \\ 3 + 2i & 7 \\ 4-18i & 6-3i \end{bmatrix}$
$B = \begin{bmatrix} 1-5i & 1+2i \\ 1-2i & 1+5i \end{bmatrix}$
$C = \begin{bmatrix} 1-7i & 4+3i & 2-8i \\ 4+6i & 1-6i & 8 + 4i \end{bmatrix}$
Here are my answers. Can someone please verify them?
$A^* = \begin{bmatrix} 1-i & 3-2i & 4+18i \\ 4+7i & 7 & 6+3i\end{bmatrix}$
$B^* = \begin{bmatrix} 1+5i & 1+2i \\ 1-2i & 1-5i \end{bmatrix}$
$C^* = \begin{bmatrix} 1+7i & 4-6i \\ 4-3i & 1+6i \\ 2+8i & 8-4i \end{bmatrix}$
None of these matrices is hermetian.
I agree with your answers and that none of the matrices is hermetian.