On Sun, 29 Feb 2004, Philip Warner wrote: > At 01:17 AM 29/02/2004, Prof Brian Ripley wrote: > >On Sun, 29 Feb 2004, Philip Warner wrote: > > > > > My understanding of SVD is that, for A an mxn matrix, m > n: > > > > > > A = UWV* > > > > > > where W is square root diagonal eigenvalues of A*A extended with zero > > > valued rows, and U and V are the left & right eigen vectors of A. But this > > > does not seem to be strictly true and seems to require specific > > > eigenvectors, and I am not at all sure how these are computed. > > > >(A %*% t(A) is required, BTW.) That is not the definition of the SVD. > >It is true that U are eigenvectors of A %*% t(A) and V of t(A) %*% A, but > >that does not make them left/right eigenvectors of A (unless that is your > >private definition). > > Sorry, that should have read 'left & right singular vectors', and I'm > beginning to suspect that they are only the starting point for deriving the > singular vectors (based on > http://www.cs.utk.edu/~dongarra/etemplates/node191.html) > > > > Since eigenvectors are not unique, it does mean that > >you cannot reverse the process, as you seem to be trying to do. > ...cut... > > > > > > which seems a little off the mark. > > > >It is not expected to work. > > Maybe not by you... 8-} > > > > >There is no rule: the SVD is computed by a different algorithm. > > So I assume my approach will not give me the singular vectors, and I need a > different way of deriving them, is that right?
I think there are ways to derive the correct signs, but your approach is a poor way to do the calculations as it squares the condition number of A. There are standard algorithms for computing the SVD from A alone. > > > Thanks for your help, it is much appreciated. > > > > > ---------------------------------------------------------------- > Philip Warner | __---_____ > Albatross Consulting Pty. Ltd. |----/ - \ > (A.B.N. 75 008 659 498) | /(@) ______---_ > Tel: (+61) 0500 83 82 81 | _________ \ > Fax: (+61) 03 5330 3172 | ___________ | > Http://www.rhyme.com.au | / \| > | --________-- > PGP key available upon request, | / > and from pgp.mit.edu:11371 |/ > > -- Brian D. Ripley, [EMAIL PROTECTED] Professor of Applied Statistics, http://www.stats.ox.ac.uk/~ripley/ University of Oxford, Tel: +44 1865 272861 (self) 1 South Parks Road, +44 1865 272866 (PA) Oxford OX1 3TG, UK Fax: +44 1865 272595 ______________________________________________ [EMAIL PROTECTED] mailing list https://www.stat.math.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide! http://www.R-project.org/posting-guide.html
