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Subject: Re: General flat-flat intersection



Kaba wrote:
> 1) What is "Geometric algebra" and how it relates to Clifford algebra
> and Grassmann algebra?
>
Geometric algebra is a term invented almost a hundred years ago by
Artin (as far as I remember). It is a branch of math covering (but not
limited to): Clifford algebras (Plural! It is not just one Clifford
algebra. Even if we fix a dimension we have a number of possible
signatures to choose from.), quaternion algebra(s) (being a special case
of Clifford algebras), Brauer-Wall group(s) and so on.

Recently it gained interest from CG and animation comunity.

In our FAQ, Ken wrote a page on it:
http://cgafaq.info/wiki/Geometric_algebra
I started to write another page almost a year ago, but never had
time to finish it:
http://cgafaq.info/wiki/Clifford_Algebra
In the section 'external links' there you can find much more stuff.

> 2) I am also reading on tensors at the moment. I have a feeling tensors
> are somehow connected to the Clifford algebra. Is there a connection and
> if there is, what is it?
>
Well, yes there is. But in fact you can connect tensors to
many areas of algebra, anyway. In a nut shell, one way to
define Clifford algebras is via tensor algebras. More modern
treatments, usually define Clifford algebras axiomatically, but
the way through tensor algebras is IMHO more intuitive. And
even with the more abstract approach, to show the existence we
revert to tensor algebras anyway (although sometimes they are
kept hidden inside more advanced structures :)

Przemek

--
"Beauty is the first test: there is no permanent place
in the world for ugly mathematics." G.H. Hardy

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