Re: Outer product in mathematica

• To: mathgroup at smc.vnet.net
• Subject: [mg51304] Re: Outer product in mathematica
• From: Jonas Sourlier <aeroswiss at gmx.net>
• Date: Thu, 14 Oct 2004 06:35:24 -0400 (EDT)
• References: <ckd5i8\$4vj\$1@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

```On Tue, 12 Oct 2004 06:05:17 +0000 (UTC), John Browne
<jbrowne at swin.edu.au> wrote:

>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 Tue, 12 Oct 2004 06:06:18 +0000 (UTC), Matteo Delfino
<delfino at studenti.ph.unito.it> wrote:

>Outer product (or tensor product) and cross product are not the same
>thing.Outer product is defined between two tensors and produces a tesor
>  of higher rank,cross product takes two vector (read:tensor of the same
>rank) and produces another vector (read:tensor of the same rank as
>before).In mathematica cross product is defined as Cross[] and Outer
>product as Outer[].

okay, thanks alot. Could it be that "outer product" in English means
only the tensor outer product, meanwhile in German "äusseres Produkt"
has more the sense of the antisymmetric tensor product
("wedge-product")? Our professor talked only about the second one...

When I tried several things with the functions Outer to get the
antisymmetric tensor product, I figured out it's possible even without
Cross:

Let u, v be vectors of R^n,

A = Outer[Times, u, v]

so A is a nxn-matrix, then set

A = A - Transpose[A]

for A becomes a skewsymmetric nxn-matrix. Then take the upper-right
components of A (without the diagonal). They are exactly the
components of the antisymmetric tensor product of u and v.

So right?

I didn't manage to use Cross for vectors of other dimension than
three, but anyway, Outer does it as well.

thanks alot, greetz Jonas

```

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