Subject: Re: CCL:lin.alg.? (basis set in the orthog. subspace)

From: Konrad Hinsen <[email-masked]>
Date: Thu, 8 Apr 1999 17:50:05 +0200

> Does anyone know the efficient algorithm/subroutine for calculating the
> basis in the orthogonal subspace?  Or, more precisely:
>   Given N M-dimensional vectors, how to find (M-N) M-dimensional
> orthonormal vectors, each of them being orthogonal to the each of the N
> original vectors.

Such a set of vectors can be obtained as a "side effect" of singular
value decomposition (SVD). I use the SVD routines in LAPACK for this
purposes. What you get is

1) A basis for the subspace spanned by the set of input vectors.
2) A basis for the complementary space, which is what you are
   looking for.

-- 
-------------------------------------------------------------------------------
Konrad Hinsen                            | E-Mail: [email-masked]
Centre de Biophysique Moleculaire (CNRS) | Tel.: +33-2.38.25.55.69
Rue Charles Sadron                       | Fax:  +33-2.38.63.15.17
45071 Orleans Cedex 2                    | Deutsch/Esperanto/English/
France                                   | Nederlands/Francais
-------------------------------------------------------------------------------