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)[reply]

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

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)[reply]

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'easter (talk) 06:55, 10 August 2020 (UTC)[reply]

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)[reply]