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Message-ID: <15447.54321.120322.757656@nanonic.hilbert.space>
From: paurea@gsyc.escet.urjc.es
To: 9fans@cse.psu.edu
Subject: Re: [OT] Re: [9fans] Getting started in Plan9 - help
In-Reply-To: <3C57AF73.727F8CE9@null.net>:Douglas A. Gwyn's message of 09:29:18 Wednesday,30 January 2002
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	<15446.32000.710318.879017@nanonic.hilbert.space>
	<3C57AF73.727F8CE9@null.net>
Date: Wed, 30 Jan 2002 12:08:33 +0100
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Douglas A. Gwyn writes:
 > As usually defined the c.p. is supposed to result in the same
 > type as its arguments, but e.g. the c.p. of two vectors is
 > *not* a vector (it's a so-called pseudo- or axial vector,

Well, as everything, depends on what you call type. Everything here
are Tensors at least. (and also vectors, because tensor spaces are
vector spaces).

Anyway I think you confusing the c.p. with the wedge product which is
it's dual in an special case. As far as I know the c.p. of two vectors
is a vector. In fact, it is the special case of aplying the dual
operator to the wedge product with N=3 and r=2, that is, the result is
also a vector in the same space, that is why it is called vector
product too.

The tensors which written as a wedge product form a tensor are called its
strict components (I think you are referring to that). Anyway, the
wedge product of a group of tensors is a tensor too. And *all* of this
operations are called products, though that is exterior algebra and maybe
the analogy has been taken a little bit too far.

--
                 Saludos,
                         Gorka

"Curiosity sKilled the cat"