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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
> > context (play around with the notion of determinants to see what
> > happen, even with mild-manered beings such as quaternions :-) ).
> Well, we 'mad physicists' even use Determinants involving grassmann
> ( anticommuting beasts ). But linear Algebra get's a "little bit
> 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
> just having "+", "-", "*", and operations like transpose() would be
> 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
> > usually known as modules and have a rich theory (and
> 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++.

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