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MathGroup Archive 2004

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Re: Outer product in mathematica

  • To: mathgroup at smc.vnet.net
  • Subject: [mg51281] Re: [mg51261] Outer product in mathematica
  • From: John Browne <jbrowne at swin.edu.au>
  • Date: Tue, 12 Oct 2004 01:57:44 -0400 (EDT)
  • References: <200410110525.BAA05003@smc.vnet.net>
  • Sender: owner-wri-mathgroup at wolfram.com

Jonas,

The function you are looking for is Cross, not Outer.

Outer in Mathematica is more like the tensor outer product, not the 
antisymmetric tensor product.


On 11/10/2004, at 3:25 PM, Jonas Sourlier wrote:

> Hi there
>
> In the lections at my University I have learnt that the outer product
> of two Vectors is defined as follows:
>
> (a)       x (b)       = 0
> (a, b)    x (c, d)    = ad - bc
> (a, b, c) x (d, e, f) = (bf - ce, cd - af, ae - bd)
>
> For two four-dimensional Vectors the outer product produces a
> six-dimensional Vector (handled as a skew-symmetric 4x4-matrix).
> The general, axiomatic definition of the outer product says that it is
>
> graduately anti-commutative: u x v = (-1)^(k+l) (v x u)
> bilinear: (u + v) x w = u x w + v x w
>
> for two vectors u, v and w with dimensions k, l, m.
>
>
> Now, my question: The outer product seems to be implemented in
> Mathematica with the function Outer. But whatever I've tried so far
> with Outer I didn't manage to get the outer product of two vectors as
> described above.
>
> Outer[Times, {a,b,c},{d,e,f}]    produces the 3x3-Matrix
>
> {{a d, a e, a f}, {b d, b e, b f}, {c d, c e, c f}}
>
> How can I calculate the outer product of two vectors with Mathematica?
>
> Thank a lot for helping me!
> Jonas
>
>
____________________________
John Browne


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