"Rotation operator part 2" R = ((1,-theta/n),(theta/n,1)) "Verify eigenvalues and eigenvectors" lambda1 = 1 + i theta / n x1 = (1,-i) x1 = x1 / sqrt(dot(conj(x1),x1)) -- normalize check(dot(R,x1) == lambda1 x1) lambda2 = 1 - i theta / n x2 = (-1,-i) x2 = x2 / sqrt(dot(conj(x2),x2)) -- normalize check(dot(R,x2) == lambda2 x2) D = ((lambda1,0),(0,lambda2)) Q = transpose((x1,x2)) check(dot(Q,D,inv(Q)) == R) "ok" Dn = ((exp(i phi),0),(0,exp(-i phi))) "Verify equation (1)" check(dot(Q,Dn,inv(Q)) == ((cos(phi),-sin(phi)),(sin(phi),cos(phi)))) "ok" Run