clear;
figure;
hold off;

%Create data 
X1 = randn(2,100);
X2 = randn(2,100);
X1 = X1 + repmat([0,3]',1,100);
X2 = X2 + repmat([0,-3]',1,100);
X = [X1 X2];
size(X)

plot(X(1,:),X(2,:),'+');
grid on;
hold on;

[U S V] = svd(X);
size(U)
size(S)
size(V)

Uk = U(:,1:2);
Sk = S(1:2,1:2);
Vk = V(:,1:2);
foo = inv(Sk)*Uk';
%normalize for plotting purposes 
foo(1,:) = foo(1,:)./norm(foo(1,:));
foo(2,:) = foo(2,:)./norm(foo(2,:));

axisLength=10;
plot([0 foo(1,1)*axisLength foo(1,1)*-axisLength],[0 foo(1,2)*axisLength foo(1,2)*-axisLength],'r')
plot([0 foo(2,1)*axisLength foo(2,1)*-axisLength],[0 foo(2,2)*axisLength foo(2,2)*-axisLength],'g')

figure
plot(Vk(:,1),Vk(:,2),'g+')
grid on;