Talk:Projection (mathematics)

For the Lay Person

I did not understand this article at all, it was very hard to read for the novice. — Preceding unsigned comment added by 195.8.168.252 (talk) 13:48, 27 October 2011 (UTC)

I second the previous comment, in particular the discussion of left inverses is not readable. If a projection is many-to-one, how does it have an inverse at all? And how does a map have a left inverse? Shouldn't it just have an inverse, period? Crisperdue (talk) 19:35, 2 September 2012 (UTC)

Notes & Queries

Jon Awbrey 16:52, 31 January 2006 (UTC) what about the inverse of projection function ? does it exist or not? —Preceding unsigned comment added by 220.227.98.203 (talk) 06:56, 11 September 2008 (UTC)

What does projection mean?

In the lead of the article it says:

a projection is any one of several different types of functions, mappings, operations, or transformations

This doesn't tell us very much. Is there a better description/definition for projection that captures the general meaning? pgr94 (talk) 07:19, 27 July 2010 (UTC)

Proposed Merge

I suggest that the new article combining dimensions be merged here. The term combining dimensions is just a naive way of referring to projection. The entire content of that article is to say that projection is a way to visualize aspects of a higher dimensional phenomenon, as is often done by certain physicists. As a use of projection, it perhaps can be dealt with here in a sentence. On its own, it will remain a stub forever. Bill Cherowitzo (talk) 19:38, 12 August 2012 (UTC)

Although this proposal is rather old, I support it. However, a better target for the merge would be Projection (linear algebra). By the way, Projection (geometry) would probably be an even better target, if the article would exist. D.Lazard (talk) 14:44, 28 June 2013 (UTC)

Wouldn't dimensionality reduction be a better target for the merge/redirect? QVVERTYVS (hm?) 11:33, 29 October 2013 (UTC)

Actually, dimensional reduction, a physics concept, would be more in line than the statistics article. However, a merge with that stub would not enlighten any reader and I hesitate to suggest it. I agree with User:D.Lazard, the right page to merge this with does not yet exist. Bill Cherowitzo (talk) 17:23, 29 October 2013 (UTC)

Merge to linear algebra

There's already a very good article at Projection (linear algebra). — Preceding unsigned comment added by Mauro Bieg (talk • contribs) 11:50, 28 June 2013 (UTC)

I oppose to this merge: Projection (mathematics) is about a concept which contains the one described in Projection (linear algebra), but is much wider. By the way, Projection (mathematics) is rather incomplete and deserve to be expanded by adding sections about

• Projection in geometry: this is related to the concept of projection in linear algebra, but different. In fact Perspective (visual) and Map projection are geometrical projections that have not really related with projection (linear algebra). IMO this concept deserve not only a section in this article, but also its own article.
• Projection in algebraic geometry: Projections are a fundamental tool in algebraic geometry, and are, in particular (but not only) the basis of Elimination theory and of Cylindrical algebraic decomposition.

D.Lazard (talk) 15:06, 28 June 2013 (UTC)

I also strongly oppose merging this general article into the specialized linear algebra page. I know what projections are in Linear Algebra. I am studying another subject and couldn't understand an implication regarding projections because they hadn't defined projections in that context. I needed the most generic definition of projection in any context (this page), so that I could apply it to this subject. This page reminded me that what I'd been taught (defining projections differently in different subjects, and then getting around to proving they're idempotent if you need to) is backwards and idempotency is not just a cute property of projections (and maybe some other operations?) in some subjects, but it's the defining feature of all projections in all subjects. Yoda of Borg (talk) 20:27, 9 April 2014 (UTC)

Splitting it up?

maybe better to split the artiicle up into

• projection (geometry) for the non-analytic geometry parts
• projection (analytic geometry) for the analytic geometry parts
• projection (mathematics) for the rest

Motivation: many geometry articles are to much analytic geometry orientated (probably because most mathematics is now a days analytic /algabraic) while the average person is much more in the geometry of models. — Preceding unsigned comment added by 213.205.230.37 (talk • contribs) 13:56, 24 January 2014‎

IMO, this article is not long enough for deserving to be split. Moreover, the different concepts of projection are strongly related, and a split would makes navigation difficult, and possibly confusing, for non-experts. On the other hand, I agree that presently, the article is confusing. It seems that the best solution would be to create clearly named sections, such that "In geometry", "In linear algebra" (with a template {{main article|Projection (linear algebra))}}), "In set theory and category theory", ... Such a structure would allows better explaining how these superficially different concepts are strongly related. Also, the lead is too long, and some parts of it, such as the definition of geometric projections, should be moved to the body.

Are you willing for starting this rewrite? D.Lazard (talk) 21:01, 28 January 2018 (UTC)