diagonalize {{0,-i,0,0,0,0,0,0}, {i,0,0,0,0,0,0,0}, {0,0,0,0,0,0,0,0}, {0,0,0,0,-i/2,0,0,0}, {0,0,0,i/2,0,0,0,0}, {0,0,0,0,0,0,i/2,0}, {0,0,0,0,0,-i/2,0,0}, {0,0,0,0,0,0,0,0}}