Talk:Outer product

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[edit] Associavity

Associativity only in the sense

(sa) x b = s(a x b),

with scalar s! Patrick 13:31 Nov 20, 2002 (UTC)

[edit] Outer product vs exterior product

Isn't this page redundant? It should be merged with exterior power. This page purports to define wedge product, however wedge product currently links to the exterior algebra page. -- Fropuff 19:34, 2004 May 20 (UTC)

The exterior product or wedge product, in the context of exterior algebra, is defined very differently from the outer product presented here today (it might have been different in 2004, qhen you wrote your comment). An outer product returns a matrix. An exterior product creates a multivector. Paolo.dL 13:07, 19 May 2007 (UTC)

[edit] Ambiguity (outer, exterior, or tensor?)

This should really be a disambiguation page, Exterior algebra is one possibility, but Tensor product is also valid. RaulMiller 18:52, 3 October 2005 (UTC)

I think it is very useful to find the definition of the outer product in a separate page, as well as for dot product and cross product. Perhaps it might be made clearer that, although outer product is a general term, with different meanings depending on the context, most people (as far as I know) tend not to associate it with the exterior product. By the way, I hypothesize that the exterior product was called exterior just to distinguish it from the outer product as defined in this article (see also Talk:Exterior algebra).
Notice that, initially, the exterior product was called by Grassmann, the German mathematician who defined it, "ausser produkt" (literally translated as "outer product", where outer has the same meaning as exterior, but is linguistically and phonetically much more similar to the German word ausser). Thus, the expression outer product, initially, was associated with the exterior product rather than with the multiplication defined in this article (the tensor product). Interestingly, as far as I know the opposite is true nowadays. Paolo.dL 13:07, 19 May 2007 (UTC)

[edit] Wrong note concerning inner product

There is an error here:

If W = V, then one can also pair w * (v), which is the inner product.

Inner product is a mapping from V \times V. Here we have mapping V^* \times V. Natural correspondence between V and V * exists only for Hilbert spaces (See Riesz representation theorem for details).

Tenzink (talk) 10:30, 22 April 2008 (UTC)

I don't think the correspondence is used here. I think that w* denotes an element of the dual space W*. (Not the dual of an element of W.) That said, the section does take a rather idiosyncratic view towards the definition of an inner product. silly rabbit (talk) 10:57, 22 April 2008 (UTC)
Agree. Tenzink (talk) 10:51, 23 April 2008 (UTC)