From: spellucci@mathematik.th-darmstadt.de (Peter Spellucci)
Newsgroups: sci.math.num-analysis
Subject: Re: Advice needed in finding vector dependance
Date: 5 May 1998 11:48:40 GMT

In article <354e1be2.0@oit.umass.edu>, lawrence@math.umass.edu (James Lawrence) writes:
|> I have n unit-length vectors each of dimension n.
|> I am looking for a number which measures how close
|> these vectors are to being dependant upon each other.
snip
|> Doing a singular value decomposition may be what I'm 
|> looking for -- perhaps looking at the middle diagonal
|> matrix for any closely-zero entries.  Is this how
|> you would do it|> 
snip
yes, using the svd is the best way to measure near linear dependence of
unit vectors. but it is costly of course (although, since you do not need the
orthogonal factors, the golub-kahan-reinsch method is quite fast. )
a cheaper approach would be to use a rank-revealing qr-decomposition.
See
Tony F. Chan, "Rank Revealing QR Factorizations", Linear Algebra and Its
Applications, 1987, Volume 88/89, pages 67--82.

A MATLAB implementation of the algorithm by Christian H. Bischof and Per
Christian Hansen may be downloaded from

http://www.mathworks.com/contrib/v4/linalg/.tarhell/rrqr.tar
hope this helps
peter