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MathGroup Archive 2002

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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


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