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I have just one question: canonical bundle is defined as the n-th exterior power of thecontangent space, would it not be more aproppriate to define the pseudoscalar as element of the n-th exterior power of thetangent (vector) space? Probably its the same, I m just confused.—Precedingunsigned comment added by195.113.34.69 (talk)14:30, 8 November 2007 (UTC)[reply]

I had written a lengthy post about confusion with the "dual" to which the writer refers. It turns out it's theHodge dual. It's not as simple as popping in a single word, so I'll try to edit it in, adjusting as little as possible, but preserving the mathematical precision, tomorrow afternoon.Warrickball (talk)22:03, 21 May 2008 (UTC)[reply]

I have removed the given Clifford algebra as the given pseudoscalar element didnot commute with the vectors.

Regarding the definition, I must confess that I'm a bit at a loss. The top-grade element of Clifford algebra commutes with all other elements and flips under parity transformationsiff the underlying basis is of odd dimension. Otherwise it doesneither. And despite having done a fair bit of reading on Clifford algebras, I'm not sure what the accepted definition of a pseudoscalar is.—Precedingunsigned comment added byStar trooper man (talk •contribs)12:03, 1 July 2009 (UTC)[reply]

I'm going to add the Clifford algebra part back in. The article seemed to be correct before. The properties of commuting with other elements and flipping under a sign change are only mentioned in the physics sections, and this context only deals with 3 dimensions (where these things happen to be true). The more general math definition as far as I can tell is simply a top-grade element. Could someone who's knowledgeable on the subject weigh in on this?Rckrone (talk)03:39, 5 August 2009 (UTC)[reply]

Please consider incorporating any useful material from the above submission into this article. The submission is eligible for deletion in 6 months. ~Kvng (talk)01:57, 20 May 2015 (UTC)[reply]

No, it has no material suitable for merging here. Despite the similarity of the word, it is to all intents unrelated in meaning. —Quondum02:08, 20 May 2015 (UTC)[reply]

As far as I know, a surface normal is defined as a cross product between two linearly independent vectors within the surface, and thus is a pseudovector itself. Accordingly, the dot product between magnetic field and surface normal is a dot product between two pseudovectors and hence a "true" scalar. Or am I missing something out?

The German wikipedia site has this example too, and it too has been questioned on the respective talk page (but not by me, that entry is older).--2003:E7:7707:490:3D96:D6F3:2396:6ED3 (talk)02:45, 25 January 2022 (UTC)[reply]

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