From help-octave-request at bevo dot che dot wisc dot edu  Wed Jan 10 07:29:38 2001
Subject: Re: question on vector product
From: "John Fletcher" <J dot P dot Fletcher at aston dot ac dot uk>
To: Rolf Fabian <fabian at tu-cottbus dot de>
CC: help-octave at bevo dot che dot wisc dot edu
Date: Wed, 10 Jan 2001 13:27:22 -0000

Date forwarded: 	Wed, 10 Jan 2001 07:12:09 -0600 (CST)
From:           	Rolf Fabian <fabian at tu-cottbus dot de>
To:             	"'help-octave UWISC'" <help-octave at bevo dot che dot wisc dot edu>
Subject:        	question on vector product
Date sent:      	Wed, 10 Jan 2001 14:08:35 +0100
Forwarded by:   	help-octave at bevo dot che dot wisc dot edu

> Hi
> 
<part snipped>
> 
> Now my  questions
> 1) What's the vector (cross)  prod in dimensions n=0,1 
> 2) What's magic with dimension n=7 ?
> Can anybody give a formulae or describe an algorithm to calculate 
> the7-dim vector (cross) product?
> 
> Furthermore a question not related to referenced article:
> 3) Even for (standard) 3-dim space, I've only found definitions for a vector (cross) product
> defined in Euklidian 3d space (real vectors only).
> What's the correct definition in unitary 3D-space (complex vectors) ?
> If any .. are there more than one possibilities for such a definition ?
> 
> Thanks
> Rolf
> 

The answer to the question is complicated.  One way of saying it is 
that the cross product is a historical accident of limited usefulness. 
There is a more general algebra which includes the cross product 
and works in any number of dimensions.  It is known as Clifford 
Algebra or Geometric Algebra.

To be more helpful than that I will add this web reference which will 
be a starting point to find out why.

http://www.mrao.cam.ac.uk/~clifford/introduction/

I hope this is helpful.

John Fletcher

-------------------------------------------------------------------
Dr John P. Fletcher          Tel: (44) 121 359 3611 ext 4625
Chemical Engineering and Applied Chemistry (CEAC),
School of Engineering and Applied Science (SEAS),
Aston University,            Fax: (44) 121 359 4094
Aston Triangle,              Email: J dot P dot Fletcher at aston dot ac dot uk
BIRMINGHAM B4 7ET  U.K.      CEAC Web site http://www.ceac.aston.ac.uk/



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