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Re: question on vector product

From: John Fletcher
Subject: Re: question on vector product
Date: Wed, 10 Jan 2001 13:27:22 -0000

Date forwarded:         Wed, 10 Jan 2001 07:12:09 -0600 (CST)
From:                   Rolf Fabian <address@hidden>
To:                     "'help-octave UWISC'" <address@hidden>
Subject:                question on vector product
Date sent:              Wed, 10 Jan 2001 14:08:35 +0100
Forwarded by:           address@hidden

> 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.

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: address@hidden
BIRMINGHAM B4 7ET  U.K.      CEAC Web site

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