Wikipedia:Articles for deletion/Matrix unit

The following discussion is an archived debate of the proposed deletion of the article below. Please do not modify it. Subsequent comments should be made on the appropriate discussion page (such as the article's talk page or in a deletion review). No further edits should be made to this page.

The result was keep. And merge with Draft:Matrix unit. Sandstein 10:04, 20 November 2021 (UTC)[reply]

Matrix unit

[Hide this box] New to Articles for deletion (AfD)? Read these primers!

(Find sources: Google (books · news · scholar · free images · WP refs) · FENS · JSTOR · TWL)

This article does not cite any sources. It has been this way since it was created in 2004, and still is when it was last editted in 2021. I cannot find a source on the Internet. If there is a source, this concept must be obscure any way, so that a source can't be found online. Mojoline (talk) 16:04, 11 November 2021 (UTC)[reply]

Note: This discussion has been included in the list of Mathematics-related deletion discussions. Shellwood (talk) 17:38, 11 November 2021 (UTC)[reply]
~~Delete~~ I don't think there is a notable concept that has to do with what this page is talking about. The three mainspace pages that link here appear to do so in error. Danstronger (talk) 17:53, 11 November 2021 (UTC)[reply]
Edit -- Delete It's a mathematical concept. It seems it will be found in lots of textbooks. Here's one example[1]. IMO the page needs sourcing, not deletion. -- Bob drobbs (talk) 19:15, 11 November 2021 (UTC)[reply]
@Bob drobbs: That's a link to an Amazon page. Do you have a copy of the book? If so, can you provide a brief synopsis of what material it contains on this topic? (It seems more likely to me that you just scraped this from a search engine result.) --JBL (talk) 19:25, 11 November 2021 (UTC)[reply]
@JayBeeEll: You should be able to read the text at that amazon link. However, upon looking further it seems that "Matrix Unit" has no relation to "Unit Matrix". I concede that matrix unit seems to be a concept in graduate level mathematics that's obscure enough, that it doesn't belong here. Changed vote. -- Bob drobbs (talk) 19:49, 11 November 2021 (UTC)[reply]
Comment this seems to be a legitimate, albeit obscure, mathematical concept. It's covered in Fundamentals of the Theory of Operator Algebra by Kadison & Ringrose and referenced as a concept in Theory of Operator Algebras III by Takesaki. Sources not being easily found online are not a reason for lack of notability per WP:OFFLINE. There seems to be a fair amount of mention of this within Operator Algebra books; however, unsure if that confers any sort of notability. Also, to be perfectly honestly, unclear if it is the same topic discussed in the article. It seems to be but I cannot definitively say. snood1205^{(Say Hi! (talk))} 20:11, 11 November 2021 (UTC)[reply]
It looks to me like the word as used by Takesaki is very likely the same concept as the topic of this article. --JBL (talk) 20:24, 11 November 2021 (UTC)[reply]
I don't think so. I think Takesaki is talking about matrices that are zero everywhere except one entry that equals 1 (" $E_{ij}$ "). (As opposed to this page which appears to be talking about the matrix shape). The $E_{ij}$ definition is supported by [2] and it is what the wikipedia pages linking here were expecting to find. If this page survives, I think it should be changed to be about that concept. Danstronger (talk) 20:42, 11 November 2021 (UTC)[reply]
A total rewrite from scratch, based on what sources say, about a different topic, seems like a very reasonable alternative to deletion. But if no one has immediate interest in writing that page, I don't think this page should remain up in it's current form. -- Bob drobbs (talk) 00:57, 12 November 2021 (UTC)[reply]

@Danstronger: I don't think it's as different as you say: the multiplication rule for square matrices with a single 1 is essentially the same as the rule for when matrices of two different shapes can multiply. --JBL (talk) 19:11, 14 November 2021 (UTC)[reply]
@JayBeeEll: Yeah, that's true, the multiplicative structure is the same between the two concepts. Danstronger (talk) 21:04, 14 November 2021 (UTC)[reply]
Comment I agree that the concept seems fine, and should be sourced and not deleted if possible, and rewritten if necessary. I thought there weren't any sources based on my not-at-all-extensive search; for that I apologize. One of the sources given here, Lectures on Modules and Rings by T. Y. Lam, is the original source of the PlanetMath page. Lectures on Modules and Rings give a definition^[1]: a set of matrices $\{e_{i,j}\}$ is a set of matrix units such that $e_{i,j}e_{l,k}=\delta _{j,l}e_{i,k}$ ; however, this definition seems to refer to general sets of matrix units while the so-called standard matrix units are just a specific one of them (similar to how the standard basis of a Euclidean vector space is just one of many bases). Except the PlanetMath page and Lectures on Modules and Rings, all other sources use matrix units as though it is common knowledge in the field and give no definitions. Although I hardly understand any of what was talked about in the sources, I am pretty confident that they all refer to the same concept given in the PlanetMath page and Lectures on Modules and Rings. As to why the wiki entry is about a whole other concept, I suspect it is because the common matrix unit can be applied to present the wiki entry matrix unit: if we interpret a common matrix unit $E_{i,j}$ as a wiki entry matrix unit $(i,j)$ , then the multilication checks out. Mojoline (talk) 04:52, 12 November 2021 (UTC)[reply]
Comment I created a stubby Draft:Matrix unit based on what seems to be the standard definition. I suggest we switch the page to this version if we keep the page. Between deleting and switching to this version, I lean slightly towards switching. Hopefully there is more to say about these matrices and someone will add it at some point. I have struck my "delete" accordingly. Danstronger (talk) 04:55, 12 November 2021 (UTC)[reply]
Thank you for making the draft! Works for me. I also struck out my delete. -- Bob drobbs (talk) 04:59, 12 November 2021 (UTC)[reply]
Keep and merge Draft:Matrix unit into Matrix unit: So in terms of an AfD resolution, the position above seems to be either:
1. Delete and then move Draft:Matrix unit to Matrix unit (if the history should not be preserved)
2. Merge Draft:Matrix unit into Matrix unit (effectively replacing it, but preserving the history)

~~Since it's a completely new article on a different topic and preserving none of the original content, I don't see why the history would need to be preserved. So delete and then move?~~ If you look closely at the part after "Another notation [...]", this original article is actually about what is described at Draft:Matrix unit. The connection of the second part of the original article to the first part of the article (essentially about matrices over singleton sets) seems to be unreferenced for now, but the rest is about integer-valued matrices with 1 at one entry and 0s at all other entries. — MarkH₂₁^talk 17:00, 12 November 2021 (UTC); updated — MarkH₂₁^talk 17:39, 12 November 2021 (UTC)[reply]

Keep by merging Draft:Matrix unit into Matrix unit to preserve history. Thank you all for your work on this. snood1205^{(Say Hi! (talk))} 18:07, 12 November 2021 (UTC)[reply]
(Non-administrator comment) History Merge per above. User:力 (powera, π, ν) 02:09, 19 November 2021 (UTC)[reply]
Option #2: Keep, use draft text, preserve history Thanks for the work. -- Bob drobbs (talk) 02:30, 19 November 2021 (UTC)[reply]
Merge Draft:Matrix unit to this title. I agree with the above proposal to replace the content and perform the necessary history merge. --Kinu ^t/_c 07:51, 20 November 2021 (UTC)[reply]

References

^ Lam, Tsit-Yuen. Lectures on Modules and Rings (1 ed.). Springer, New York, NY. p. 461. ISBN 978-1-4612-0525-8. Retrieved 12 November 2021.

The above discussion is preserved as an archive of the debate. Please do not modify it. Subsequent comments should be made on the appropriate discussion page (such as the article's talk page or in a deletion review). No further edits should be made to this page.

[1] Lam, Tsit-Yuen. Lectures on Modules and Rings (1 ed.). Springer, New York, NY. p. 461. ISBN 978-1-4612-0525-8. Retrieved 12 November 2021.

[1]