       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

```

• Prev by Date: Re: Strange PV results from Integrate
• Next by Date: Re: normal distribution random number generation
• Previous by thread: Outer product in mathematica
• Next by thread: Re: Outer product in mathematica