% 
% Written by:
% -- 
% John L. Weatherwax                2005-08-04
% 
% email: wax@alum.mit.edu
% 
% Please send comments and especially bug reports to the
% above email address.
% 
% Epage 
% 
%-----

close all; clc; clear; 

X = [ 1, 2; 2, 1; 1, 3 ]; 
X' * X
X * X' 

[xtx_evec,xtx_eval] = eig( X' * X )
[xxt_evec,xxt_eval] = eig( X * X' ) 

% One has to match the eigenvectors of X X^H and X^H X to use in the inner product 
% by the eigenvalues each one has.
%
Xhat = sqrt(xtx_eval(2,2)) * ( xxt_evec(:,3) * (xtx_evec(:,2)') ) + ... 
       sqrt(xtx_eval(1,1)) * ( xxt_evec(:,2) * (xtx_evec(:,1)') )