close all; theta1 = pi/6; theta2 = pi/3; V = [cos(theta1), -sin(theta1); sin(theta1), cos(theta1)]; U = [cos(theta2), -sin(theta2); sin(theta2), cos(theta2)]; S = mdiag(2, 0.5); M = U*S*V'; %M = rand(2,2) [U,S,V] = svd(M); a_hist = []; b_hist = []; for theta=0:0.1:2*pi a = [cos(theta); sin(theta)]; b = M*a; figure(1); plot(a(1), a(2), 'bo', b(1), b(2), 'r*'); hold on; end figure(1); plot([V(1,1); 0], [V(2,1); 0], 'b-', [V(1,2); 0], [V(2,2); 0], 'b--'); plot([S(1,1)*U(1,1); 0], [S(1,1)*U(2,1); 0], 'r-', [S(2,2)*U(1,2); 0], [S(2,2)*U(2,2); 0], 'r--'); grid on;