"Verify 37.2" sigma1 = ((0,1),(1,0)) sigma2 = ((0,-i),(i,0)) sigma3 = ((1,0),(0,-1)) sigma = (sigma1,sigma2,sigma3) epsilon1 = ((0,0,0),(0,0,1),(0,-1,0)) epsilon2 = ((0,0,-1),(0,0,0),(1,0,0)) epsilon3 = ((0,1,0),(-1,0,0),(0,0,0)) epsilon = (epsilon1,epsilon2,epsilon3) J = 1/2 sigma K = i/2 sigma -- use a and b instead of i and j because i is imaginary unit for(a,1,3,for(b,1,3, check(dot(J[a],K[b]) - dot(K[b],J[a]) == i dot(epsilon[a,b],K)))) for(a,1,3,for(b,1,3, check(dot(K[a],K[b]) - dot(K[b],K[a]) == -i dot(epsilon[a,b],J)))) J = 1/2 sigma K = -i/2 sigma for(a,1,3,for(b,1,3, check(dot(J[a],K[b]) - dot(K[b],J[a]) == i dot(epsilon[a,b],K)))) for(a,1,3,for(b,1,3, check(dot(K[a],K[b]) - dot(K[b],K[a]) == -i dot(epsilon[a,b],J)))) "ok" Run