[Date Prev][Date Next][Thread Prev][Thread Next][Date Index][Thread Index]
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.
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: address@hidden
BIRMINGHAM B4 7ET U.K. CEAC Web site http://www.ceac.aston.ac.uk/
-------------------------------------------------------------
Octave is freely available under the terms of the GNU GPL.
Octave's home on the web: http://www.octave.org
How to fund new projects: http://www.octave.org/funding.html
Subscription information: http://www.octave.org/archive.html
-------------------------------------------------------------