% Sample script for typical in-class second-try to implement
% Graham Schmidt Orthogonalization in one special example.
% Now using some matrix language.
%
% All rights reserved.    Original version: Nov 2003
% Matthias Kawski         http://math.asu.edu/~kawski

V=5-round(10*rand(7,4))
check=rref(V)
Q=V
w=V(:,1)
Q(:,1)=w/sqrt(w'*w)
w=V(:,2)
w=w-(Q(:,1)'*w)*Q(:,1)
Q(:,2)=w/sqrt(w'*w)
w=V(:,3)
w=w-(Q(:,1)'*w)*Q(:,1)-(Q(:,2)'*w)*Q(:,2)
Q(:,3)=w/sqrt(w'*w)
w=V(:,4)
w=w-(Q(:,1)'*w)*Q(:,1)-(Q(:,2)'*w)*Q(:,2)-(Q(:,3)'*w)*Q(:,3)
Q(:,4)=w/sqrt(w'*w)
check=Q'*Q