Talk:Two-vector

Removed Orphan Notice
Added a link to this Article in Exterior algebra. Not sure, if this is legit, though. The mentioned "2-vector" in exterior algebra might be a bivector.--Malibu9 (talk) 12:45, 27 March 2019 (UTC)

Confused concept / notability
This article is a confusion between the concepts of a type-(2,0) tensor and a bivector. For example, the dual of a 2-form is a bivector (2-vector) field on a manifold. A bivector can be identified with an alternating type-(2,0) tensor (i.e. it can be regarded as a type-(2,0) tensor, but with the restriction of being alternating).

A second question arises: is the term "two-vector" notable, other than in the meaning of bivector? I doubt it. In which case, this article should not exist, as per WP:GNG. Both ideas (a type-(2,0) tensor and a bivector) are already adequately covered in suitable articles.

Pinging as article creator. Pinging, as someone with mathematical background who indicated that it is not to be confused with bivector. —Quondum 22:00, 7 August 2020 (UTC)


 * Striking first comment above: I was misled by the link two-form, which is a redirect to Differential form.
 * My main point remains: this article, which essentially suggests that "two-vector" is a notable name for a type-(2,0) tensor (and that this is distinct from "2-vector", which may be identitified as an alternating type-(2,0) tensor), is IMO a candidate for deletion, and I may WP:PROD or redirect it soon if no-one objects. I see that the related two-form was scrapped.  —Quondum 17:58, 8 August 2020 (UTC)
 * I feel like I've seen "two-vector" used with multiple distinct meanings (in higher category theory, or for points in 1+1-dimensional Minkowski spacetime, etc.), and the meaning in this article is not the preeminent one. My inclination would be to scrap the page. XOR&#39;easter (talk) 06:55, 10 August 2020 (UTC)
 * I'm not familiar with the use in category theory, but your second example sounds like an instance of the shorthand "three-vector" meaning element of a three-dimensional (typically Euclidean) vector subspace, used in somewhat pedagogical relativity articles to distinguish them from "four-vector". There is also two-point tensor/double vector, which is essentially the meaning described in this article.  —Quondum 12:10, 10 August 2020 (UTC)