Hi, I noticed that the first element of an orthogonal matrix extracted from the qr() function is always negative, whatever the initial matrix and its size. The other elements do not have fixed signs though.
In the simple code below, j=0 always.
j=0;for i=1:1:100000[Q,~] = qr(randn(3,3));if Q(1,1)>=0j=j+1;elseendenddisp(j)
Why is that so ?