clc;
clear;
close all;

% Generate Date
W = randn(1000, 2);
A = rand(2, 2);
X = W*A;

% Covariance Matrix
C = cov(X);

% Find PC1
[V, E] = eig(C);
[emax, emax_ind] = max(diag(E));
u = V(:, emax_ind);

% Transform Data
z = X*u;

% Decode Data
Y = z*u';

% Plot Results
figure;
scatter(X(:,1), X(:,2))
hold on;
plot(Y(:,1), Y(:,2),'r')