Talk:Tensor product

message: Well, maybe that's an overstatement, but it appears as though mathematicians have clogged this page up with soggy, pointless math jargon and made it irritatingly difficult to use as a reference for, you know, actually calculating things with tensor products. If all else fails, can somebody actually push the examples to the top as a quick reference and push the frivalous tedium to the bottom, or even better, package the frivalous tedium into a completely separate page? Or give me permission to do so.
:THIS PAGE IS THE BEST I′VE FOUND ANYWHERE ON THE INTERNET FOR NON-MATHEMATICIANS.  PLEASE KEEP IT AVAILABLE AS IS, UNDER ANOTHER NAME IF YOU MUST.  I′m a physicist who has been studying and using tensors and tensor products on and off over several years. I′ve used practically every major site and pdf on the Inet, as well as many texts, to try to break thru mathematicians' jargon and abstraction, and the more limited understanding of others, to get to a clearer understanding of the finer points, and EXAMPLES. After discovering this page it′s replaced Gower′s as the one I go to whenever I need a refresher.  IMHO it starts simply, at the best point, with just 2 vector spaces, and builds logically from there, and has a splendid set of links to further details such as Hilbert spaces TP and topological spaces TP etc. It includes excellent examples, and does include enough of the mathematical concerns in later sections to make you aware of them and where to go for more detail.  If it′s incorrect anywhere then certainly those places should be corrected, but for me it′s far superior pedagogically to anything else available on this subject.  Relabel it ″Tensor Products for Non-mathematicians″ if necessary, but please, please keep it available. JHE-37 (talk) 17:58, 10 October 2021 (UTC)
replies: text: Only the second interpretation is correct. A definition of the tensor product is given somewhere in the article, but it is rather difficult to find it. From the content of this talk page and the tags at the top of the article, it seems that everybody agree thay the article is awfully written. The problem is to find an expert that is willing to find the time for rewriting the article. D.Lazard (talk) 11:23, 5 February 2022 (UTC)
thread_title: This page is poorly constructed

message: I made the fonts consistent in this edit https://en.wikipedia.org/w/index.php?title=Tensor_product&type=revision&diff=1111854170&oldid=1111816282 now undone by an editor of the article.
My reason was that the inconsistent font uses that have been restored by that undoing editor of the page are confusing. The weak point is where the Latin lower case letter vee in the undoing editor's inconsistently preferred math markup  looks like the Greek lower case letter nu in fonts that are clearer, such as that of ·. This is evident in this snip from the article: "An element of the form v \otimes w is called the tensor product of  and ." The problem is that the two different math markup formats, · and , use different fonts. It is true that, often enough, the font usage that is inconsistently preferred by the undoing editor is slightly quicker to type. My experience is that the LaTeX format · is to be preferred as it often is in the article. Chjoaygame (talk) 11:22, 23 September 2022 (UTC)
thread_title:  inconsistent font usage 

message: In the definition from bases, it says:
The tensor product V \otimes W of  and  is a vector space which has as a basis the set of all v\otimes w with v\in B_V and w \in B_W. 
Out of the blue appears the tensorproduct v\otimes w, just the thing that should be defined. Madyno (talk) 12:33, 25 November 2022 (UTC)
replies: text: One usage of the symbol \otimes is for vector spaces; the other is for vectors. For basis vectors  v\in B_V  and  w\in B_W  the expression v\otimes w, which is a basis vector for  V\otimes W , should be thought of as a primitive symbol that doesn't reduce to anything simpler. Elements of  V\otimes W  are sums of such symbols with numerical coefficients. You can of course take the tensor product of non-basis vectors—the result will be written in terms of tensor products of basis vectors, as described in the paragraphs following the one containing the passage you quoted. I think it would be helpful to many readers if some elementary examples could be added to the article showing how the notation works and what it is useful for. Will Orrick (talk) 03:48, 26 November 2022 (UTC)
thread_title:  Definition 

message: The article defines tensor products of a finite nonnegative integer n vector spaces for only the case n=2. However, the "General tensors" section uses tensor products for general n, so we need to define somewhere tensor products in general (finite nonnegative integer). Thatsme314 (talk) 19:31, 17 October 2023 (UTC)
replies: text: The case n > 2 is defined in section . D.Lazard (talk) 20:48, 17 October 2023 (UTC)
replies: text: Good catch! Now, we just need to define it for n=0. Also, it might be nice to re-organize the article to emphasize the general definition. Thatsme314 (talk) 01:00, 18 October 2023 (UTC)
thread_title:  Tensor product of n vector spaces for n>2