Talk:Vector space

message: Vector (mathematics and physics) is being setup in summary style, so that broad-concept article should not introduce anything that is absent here. fgnievinski (talk) 05:52, 1 November 2021 (UTC)
thread_title:  Merge list of related vector concepts 

message: As I understand the word "generalization" in math, one says that objects of type A generalize objects of type B if certain A-objects are B-objects. So:
* it is perfectly correct to say that modules generalize vector spaces.
* Affine spaces do not generalize vector spaces; any vector space defines an affine space, but it is not the case that certain affine spaces are vector spaces.
* One could consider those certain vector bundles in which the base space is a point (I note this is not even mentioned in the article), and to then identify the total space with a vector space. It may be overly pedantic to say that the extra specification of the particular point matters, but I think it is simply true. It may be more correct to say that "vector space" is generalized by the concept of total space of a vector bundle, and not by vector bundle itself.
Sorry for the pedantry, but the article seems to suggest that all three concepts are equally well generalizations of vector space, and maybe this is not so good. Gumshoe2 (talk) 07:23, 15 February 2022 (UTC)
replies: text: D.Lazard (talk) 10:08, 15 February 2022 (UTC)
thread_title:  "Generalizations" section 

message: The redirect Abstract vector space has been listed at redirects for discussion to determine whether its use and function meets the redirect guidelines. Readers of this page are welcome to comment on this redirect at  until a consensus is reached.  Hildeoc (talk) 00:59, 24 June 2023 (UTC)
thread_title:  "[[:Abstract vector space]]" listed at [[Wikipedia:Redirects for discussion|Redirects for discussion]] 

message: They are supposed to be axioms. Given the amount of time vector spaces have been defined, I would assume there would be a counterexample showing some mathematical object satisfying all axioms except one. 
Counterexample help understanding just as much as examples. Sometimes more. It certainly would be helpful for me. Ndhananj (talk) 22:57, 20 August 2023 (UTC)
thread_title:  Counterexamples of mathematical structures for each axiom failing while meeting all the remaining ones 

message: The definition erroneously said there are two binary operations, one of which is scalar multiplication. In fact, the group of units of the field produces a group action on the vectors. Inclusion of zero for scalar multiplication annihilates the vector space to the zero vector. Binary operations require one set, but scalar multiplication starts with two: F and V. Precision is mathematics is expected, and this hitch of imprecision might have led to confusion.  Reference has been made to binary function since introduction of group action at this level assumes much of the reader. — Rgdboer (talk) 02:41, 22 December 2023 (UTC)
replies: text: Please, read the third paragraph of Binary operation. If you find it erroneous, you must discuss it on that talk page. In any case, most textbooks call scalar multiplication a binary operation. 09:49, 22 December 2023 (UTC)

text: As far as I know, most textbooks on vector spaces use "binary operation" for the sclar multiplication, and not "binary function". So, Wikipedia must follow the common usage. D.Lazard (talk) 09:01, 27 December 2023 (UTC)
thread_title: Scalar multiplication is not a binary operation

message: @Dedhert.Jr Thank you very much for your efforts on this article! What exactly though is the rationale behind the rearrangement of the second section? It seems to me to be a lot more difficult to understand in the new, compressed form, and for instance the definition of linear independence as "the linear combination that is equal to zero" has little resemblance to the usual definition, according to which a set of vectors is linearly independent if there is no non-trivial linear combination of those vectors that equal 0. Felix QW (talk) 19:03, 3 February 2024 (UTC)
replies: text: @Felix QW My opinion about rearrangement is that there are some relation between basis and linear combination, and this could be explained in one single paragraph rather than described in list. Dedhert.Jr (talk) 06:16, 4 February 2024 (UTC)
replies: text: I partially reverted the change for now, as I think it is important to have correct and clear definitions of the basic concepts in our vector space article. While I think the structured pairs of concept and definition work well, I would be fine with any other layout, as long as the definitions themselves are preserved. Felix QW (talk) 08:28, 4 February 2024 (UTC)
replies: text: @Felix QW You partially reverted the edit, but it could also mean that you deleted more citations to be added. Can you please add them up? Dedhert.Jr (talk) 09:25, 4 February 2024 (UTC)
replies: text: @Felix QW Nevermind. I will added it later. Dedhert.Jr (talk) 09:38, 4 February 2024 (UTC)
thread_title:  Section 2 

message: The presentation of the definition is not very good. A clear definition should IMHO mention all the components used. Furthermore, writing scalar multiplication not explicitly might be okay when working with vector spaces daily, but a definition should make this explicit.
Also in the table of "axiom" the header "meaning" is a bit misleading, like that there is some room for interpretation, but actually whats given in the column is the definition. 132.176.73.161 (talk) 06:56, 19 April 2024 (UTC)
replies: text: I do not understand your second concern, since the word "meaning' does not appear in the article. I do not understand either your first concern. By "component", I suppose that you mean coordinates on a basis. This cannnot appear in the definition since not all bases are finite, and many vector spaces do not have a given basis. For example, the real valued functions with the reals as domain form a vector space for which no basis can be explicitly described. D.Lazard (talk) 13:20, 19 April 2024 (UTC)
thread_title:  Presentation of the Definition