Talk:Euclidean subspace

I was working on a revision of linear subspace, and I found that the material naturally bifurcates (at least in my mind) into things having to do with Rn and things having to do with general vector spaces. This is the part about subspaces of Rn. Now that it's done, I think it makes a nice summary article for a wide swath of elementary linear algebra.

I haven't yet linked to this article from anywhere else. I'm planning to go through the links to the linear subspace article and determine which ones ought to go here. Jim 09:00, 2 September 2007 (UTC)

I've now updated some of the links from other pages. Jim 21:25, 11 September 2007 (UTC)
 * Thanks for this last message. Now it will be easier for us to cleanse consequences [ of these edits] given we know who and when injected this non-standard term into Wikipedia. Incnis Mrsi (talk) 20:51, 27 April 2013 (UTC)

The article is completely wrong
The article’s lead says a Euclidean subspace is simply a linear subspace of a Euclidean space and all the article pursues this heresy. Why could authors not realize that Euclidean space is a special case of an affine space? Than Euclidean subspaces are, in fact, affine subspaces? That all equations need a non-zero right side? The article teaches some stuff related to linear subspaces, not really important things one should say about Euclidean subspaces. I’ll fix all these abominations soon. Incnis Mrsi (talk) 06:47, 27 April 2013 (UTC)


 * This is an article about linear subspaces about R^n. If you disagree with the title, then propose a title change (rather than changing the entire article).. Only if you have sources that disagree with this title, of course. Mark M (talk) 07:41, 27 April 2013 (UTC)


 * There is nothing special in linear subspaces in $R^{n}$ which cannot (or should not) be covered by the linear subspace article, so I do not see any sense in the proposed change of title. You are not in a position to impose your vision what the article is about upon other editors. If the community decides that the article should be changed, I’ll change the entire article. Incnis Mrsi (talk) 08:18, 27 April 2013 (UTC)


 * You are not in a position to impose your vision what the article is about upon other editors. Hmm.. likewise? I would be in favour of merging this article into linear subspace.. then you could create a new article about affine subspaces, if you wish. But changing the scope of this article and then rewriting the whole thing does not seem to be a good use of time. Mark M (talk) 09:48, 27 April 2013 (UTC)
 * It is not a question of someone's "vision". The point is that the article uses a terminology which is WP:OR and contradicts the common usage of mathematicians: The whole article is written as if an Euclidean space were a vector space and had a natural origin. This is wrong, as pointed out in the last paragraph of Euclidean space. IMO the article must be merged into linear subspace (there is nothing in the article that depends on the basis field), and the title must be redirected to flat (geometry). D.Lazard (talk) 10:01, 27 April 2013 (UTC)
 * Flat (geometry)… good point! I did not notice this article. I go to Euclidean space now and change links to it. Incnis Mrsi (talk) 10:06, 27 April 2013 (UTC)
 * Let’s consider what we have now:
 * The linear subspace article is severely short of useful stuff
 * The Euclidean subspace article describes linear subspaces in the real coordinate space, which have not anything specific to real numbers, as I can see (ignoring the second issue that it is a misnomer)
 * There is no useful content about Euclidean subspaces proper (such as a definition of angle between two such subspaces, or one of distance between a subspace and a point, at least there is no such content under the correct title
 * What do you, Mark M, propose? Move the present article to linear subspaces of the real n-space or so, and then merge (or not) to linear subspace? Create a new article about true Euclidean subspaces, under the freed title or some another one? Just ignore the problem and leave all the crap at rest? Incnis Mrsi (talk) 10:06, 27 April 2013 (UTC)
 * As I said, I would be in favour of merging this article into linear subspace. And as D.Lazard said, redirecting the title to Flat (geometry) seems to make the most sense. Mark M (talk) 18:47, 27 April 2013 (UTC)