Re: ublas : double * matrix

From: jhrwalter (walter_at_[hidden])
Date: 2002-01-24 05:36:06

--- In boost_at_y..., Peter Schmitteckert (boost) <boost_at_s...> wrote:
> Salut,
> 
> On Wednesday 23 January 2002 00:07, hubert_holin wrote:
> >  Bonsoir
> >
> >   One can extend the usual definition of vector spaces in
> > several ways.
> >
> >   On the one hand, one can certainely use non-commutative base
> > fields. Unfortunately, most of Linear Algebra breaks down in such 
a
> > context (play around with the notion of determinants to see what 
can
> > happen, even with mild-manered beings such as quaternions :-)  ).
> Well, we 'mad physicists' even use Determinants involving grassmann 
algebras
> ( anticommuting beasts ). But linear Algebra get's a "little bit 
more 
> involved" then, since you have to introduce some kind of ordering to
> keep track of commutations. But if a matrix libraries already takes
> care of not changing orders that would be fine. 

Oops. We'll have to check that.
 
> Note, that I'm not propsing to write an LA-Package for theses 
things,
> just having "+", "-", "*", and operations like transpose() would be 
fine
> for playing with some ideas.
> 
> >   It is far more fruitfull to use a structure not based upon a
> > field, but upon a (commutative) ring, say Z/4Z. These structures 
are
> > usually known as modules and have a rich theory (and 
applications).
> 
> SU(2) would be more fruitful more me, but anyway this refers to the
> 'fun part', aka 'not so important'.

I'm not sure, if such an example wouldn't show some of the advantages 
when using C++.
 
Regards
 
Joerg