Re: cross product
- To: mathgroup at smc.vnet.net
- Subject: [mg35371] Re: cross product
- From: Jens-Peer Kuska <kuska at informatik.uni-leipzig.de>
- Date: Wed, 10 Jul 2002 02:19:34 -0400 (EDT)
- Organization: Universitaet Leipzig
- References: <agegtd$p8i$1@smc.vnet.net>
- Reply-to: kuska at informatik.uni-leipzig.de
- Sender: owner-wri-mathgroup at wolfram.com
Hi,
since Cross[] is
Table[
Sum[Signature[{i, j, k}]*x[j]*y[k], {j, 1, 3}, {k, 1, 3}], {i, 1,
3}]
your 4 d cross product of two vectors is a matrix
Table[
Sum[Signature[{i, j, k, l}]*x[k]*y[l], {k, 1, 4}, {l, 1, 4}], {j, 1,
4}, {i, 1, 4}]
Setting the _[4] component to 1 with
Table[Sum[Signature[{i, j, k, l}]*x[k]*y[l], {k, 1, 4}, {l, 1, 4}], {j,
1,
4}, {i, 1, 4}] /. _[4] :> 1
gives you the matrix you wish.
Regards
Jens
Umby wrote:
>
> Hi group,
>
> how can I achieve the CrossProduct of two 4*1 vectors (in homogeneous
> coordinate)?
> For instance: CrossProduct[{a,b,c,1},{d,e,f,1}]
> Thanks in advance
>
> Umby