I have an 8*8 Hermitian matrix and I want to Block diagonalize it to four 2*2 matrices. Is there any general way to do that?! If it's not please help me for the specific one that is posted bellow.(" i " stands for imaginary unit)
\begin{bmatrix} J-\mu & a+ib & M & 0 & 0 & 0 & 0 & 0 \\ a-ib & -J-\mu & 0 & M & 0 & 0 & 0 & 0\\ M & 0 & J-\mu & -a-ib & 0 & 0 & 0 & P \\ 0 & M & -a+ib & -J-\mu & 0 & 0 & -P & 0 \\ 0 & 0 & 0 & 0 & -J+\mu & a-ib & -M & 0 \\ 0 & 0 & 0 & 0 & a+ib & J+\mu & 0 & -M \\ 0 & 0 & 0 & -P & -M & 0 & -J+\mu & -a+ib \\ 0 & 0 & P & 0 & 0 & -M & -a-ib & J+\mu \\ \end{bmatrix},
and I want to covert it to :
\begin{bmatrix} A & B & 0 & 0 & 0 & 0 & 0 & 0 \\ C & D & 0 & 0 & 0 & 0 & 0 & 0\\ 0 & 0 & E & F & 0 & 0 & 0 & 0 \\ 0 & 0 & G & H & 0 & 0 & 0 & 0 \\ 0 & 0 & 0 & 0 & H & I & 0 & 0 \\ 0 & 0 & 0 & 0 & J & K & 0 & 0 \\ 0 & 0 & 0 & 0 & 0 & 0 & L & M \\ 0 & 0 & 0 & 0 & 0 & 0 & N & O \\ \end{bmatrix},