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Re: Outer product in mathematica

  • To: mathgroup at
  • Subject: [mg51281] Re: [mg51261] Outer product in mathematica
  • From: John Browne <jbrowne at>
  • Date: Tue, 12 Oct 2004 01:57:44 -0400 (EDT)
  • References: <>
  • Sender: owner-wri-mathgroup at


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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