function [Q, R] = GSmodificat(A)
[m, n] = size(A);
Q = A;
R = zeros(n);
for k = 1 : n
    R(k, k) = norm(Q(:, k));
    Q(:, k) = Q(:, k) / R(k, k);
    for j = k + 1 : n
       R(k,j)=Q(:,k)'*Q(:,j);
       Q(:, j) = Q(:, j) - Q(:, k) * R(k, j);
    end
end