Hi, I'm attempting to implement a QR factorization with column pivoting so that the returned R matrix has decreasing diagonal elements (that is, $r_{i,i} \leq r_{i-1,i-1}$ for all $i\geq 2$). Mathematically, it would involve finding the matrix $P$ so that $AP=QR$, or $A=QRP^T$. I'm using Gram-Schmidt to compute QR.

One source I found was this: http://www.mathworks.de/matlabcentral/newsreader/view_thread/250632

Quote from the answer:
"During the iteration #k, it is easy to show that if we pick among the set of remaining vectors (i.e., not yet included in the span) the vector that has the *largest* orthogonal component to the current subspace (generated by k first vectors), then the diagonal of R must decrease."

Sounds simple enough, but HOW do I determine which vector of the remaining ones that have the largest orthogonal component to the subspace that's already been found?

Thanks a lot in advance for any help on this matter!

Best regards Hallgeir