Talk:Linear span

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Page title[edit]

This page (span) should really be a subpage under linear algebra or vector space, since it is a restricted technical definition which meaningless out of context (critical in context though).---- Span occurs not as a separate page but as an alternate word for "generate" on the Linear Algebra page under Generating a Vector Space.

No, this page should be renamed "span (mathematics)" or "span (linear algebra)" as soon as the newest UseModWiki version is turned on...

Rewrite[edit]

I did a rewrite of the page and merged in material from linear combination. Linear span is important enough to deserve a page of its own and linear combination became to cluttered anyway.

I think the proofs should not be on this page but I did not have to courage to delete them. They are very simple and are probably done by every student taking a linear algebra course so they do not contain interesting information. But they could be put on a new page like Basics proofs in linear algebra to help a student get started in the field.

On a different note is it just me or are all the linear algebra articles in a very sorry state ? MathMartin 22:52, 2 Sep 2004 (UTC)

Link at the bottom doesn't work[edit]

Just thought I'd point that out.

Finite Dimension?[edit]

Why do we need finite dimensions for a vector space to be spanned by a set? --130.83.219.136 09:20, 2 February 2007 (UTC)[reply]

Indeed, we don't!

The statement was entered when the main definition of linear span was switched here from the set of all linear combinations of elements in S to the intersection of all subspaces containing S. As you can see, earlier there were some distinction of the finite case for other reasons, and I suspect that this inter alia yielded this redundant condition here.

Actually, I do not think that the definition switch was necessary. The trouble with the linear combinations definition is the case where S is the empty set. As noted in later edits, this is no real obstacle, if we employ the natural definition of an empty sum. It is worth a remark, though.nbsp;JoergenB (talk) 20:39, 21 August 2008 (UTC)[reply]

vs Affine hull[edit]

Is this the same as affine hull? If so then perhaps they should be merged, otherwise they could be compared (and linked). Perhaps they are the same if the field K is R. Ravelite (talk) 15:24, 10 February 2010 (UTC)[reply]

No, they are different. The affine hull of {(1,0),(0,1)} is the line x+y=1; the span of that same set of vectors is the whole plane. In general, the span of S is the affine hull of S \union \vec{0}. — Preceding unsigned comment added by 137.150.93.11 (talk) 16:44, 22 October 2019 (UTC)[reply]

Non-trivial examples?[edit]

Span(E) is defined as the intersection of all linear subspaces containing E. Could someone please include an example of a space that is "bigger" than the set in question (E), which is projected when intersections are taken (i.e. only the "common" subspaces of that space are concerned because the intersection removes "uncommon" parts). Because often people think linear combinations (the equivalent definition) should increase the span and therefore a union of sets may seem more appropriate (which is obviously wrong). Brydustin (talk) 18:22, 14 February 2012 (UTC)[reply]

Image for this page[edit]

I found this page and thought it was super helpful for visualizing vector spans. Do you think a gif of something similar (quick example) would work for a page image? 47.145.148.47 (talk) 06:43, 7 March 2018 (UTC)[reply]

The images you found are good illustrations of the sum of two vectors. The article linear subspace contains many of the concepts needed to understand this article. Since there was no image for this article, one has now been added to clarify the notion of span as used in linear algebra. — Rgdboer (talk) 02:09, 8 March 2018 (UTC)[reply]