% Straight-forward implementation of the 
%classical Gram-Schmidt orthogonalization:

function Q = GS(V,m)

[rows,cols]=size(V);
Q=zeros(rows,min(m,cols));
u =V(:,1);
nu=norm(u);
Q(:,1)=u/nu;

for k=2:min(m,cols),
    u = V(:,k);
    for l=1:k-1,
        cor(l)=Q(:,l)'*u;
        u = u - cor(l)*Q(:,l);
    end
    nu=norm(u);
    Q(:,k) = u/nu;
end
%