Outer product in mathematica

*To*: mathgroup at smc.vnet.net*Subject*: [mg51261] Outer product in mathematica*From*: Jonas Sourlier <aeroswiss at gmx.ch>*Date*: Mon, 11 Oct 2004 01:25:20 -0400 (EDT)*Sender*: owner-wri-mathgroup at wolfram.com

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

**Follow-Ups**:**Re: Outer product in mathematica***From:*Matteo Delfino <delfino@studenti.ph.unito.it>

**Re: Outer product in mathematica***From:*John Browne <jbrowne@swin.edu.au>