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

function Q = MGS(V,m)

Q(:,1:m) = V(:,1:m);
nn=zeros(m,m);
for k=1:m
    n(k,k) = norm(Q(:,k));
    Q(:,k)=Q(:,k)/n(k,k);
    for l=k+1:m
        nn(k,l)= Q(:,k)'*Q(:,l);
        Q(:,l) = Q(:,l) - nn(k,l)*Q(:,k);
    end
end
        
%