Wikipedia:Articles for deletion/Quaternionic matrix: Difference between revisions
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:''The following discussion is an archived debate of the proposed deletion of the article below. <span style="color:red">'''Please do not modify it.'''</span> Subsequent comments should be made on the appropriate discussion page (such as the article's talk page or in a [[Wikipedia:Deletion review|deletion review]]). No further edits should be made to this page.''
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The result was '''keep'''. -- '''[[User:Cirt|Cirt]]''' ([[User talk:Cirt|talk]]) 04:24, 9 September 2010 (UTC)
===[[Quaternionic matrix]]===
:{{la|Quaternionic matrix}} – (<includeonly>[[Wikipedia:Articles for deletion/Quaternionic matrix|View AfD]]</includeonly><noinclude>[[Wikipedia:Articles for deletion/Log/2010
:({{Find sources|Quaternionic matrix}})
Unsourced with no indication of notability. Seems like fairly trivial OR to me: quaternions in a 2x2 matrix, and a Google search turns up nothing like this. <small>[[User:JohnBlackburne|JohnBlackburne]]</small><sup>[[User_talk:JohnBlackburne|words]]</sup><sub style="margin-left:-2.0ex;">[[Special:Contributions/JohnBlackburne|deeds]]</sub> 11:18, 31 August 2010 (UTC)
*'''Keep''': A trivial [http://scholar.google.com/scholar?q=%22quaternionic%20matrix%22&um=1&ie=UTF-8&sa=N&hl=en&tab=ws Google Scholar search] returns tons of academic papers on the subject (the Google of the nominator must have been broken {{=)}}). The information on the matrix multiplication is far from being trivial (at least for non-mathematicians). --[[User:Cyclopia|<
*: Please, show at least one link which deals with so named "octonionic product", either for quaternions or for matrices over another non-commutative ring. If there are no sources on such structure, then it must be removed and the rest of article become a trivial application of the [[matrix ring]] concept to the quaternions division ring. [[User:Incnis Mrsi|Incnis Mrsi]] ([[User talk:Incnis Mrsi|talk]]) 07:13, 2 September 2010 (UTC)
*::Problems that can be dealt with editing are not a reason to delete, [[WP:ATD|per deletion policy]]. Feel free to remove OR from the article. --[[User:Cyclopia|<
* '''comment''' I did search, though a normal one not a scholar one, and turned up some of the same papers. But I could not find a definition, other than it's just a matrix of quaternions, or find anything that looked like this article (most of the articles seemed to be on more general n×n matrices). [http://www.google.co.uk/search?q=%22Hamiltonian+product%22+%22quaternionic+matrix%22 A search] on both "Hamiltonian product" and "quaternionic matrix" turns up only mirrors of this page and [http://scholar.google.co.uk/scholar?q=%22Hamiltonian%20product%22%20%22quaternionic%20matrix%22 a scholar search] turns up nothing. So while the term exists much of the article seems unsourced. It would be good to hear from the page creator on this, as although as it stands it looks like OR it also looks like reasonable maths that could be sourced somewhere.--<small>[[User:JohnBlackburne|JohnBlackburne]]</small><sup>[[User_talk:JohnBlackburne|words]]</sup><sub style="margin-left:-2.0ex;">[[Special:Contributions/JohnBlackburne|deeds]]</sub> 19:07, 31 August 2010 (UTC)
** I don't understand where did you get the impression that the article is only on 2x2 matrices. --[[User:Cyclopia|<
***The definition ("matrix of quaternions") applies in any dimension and the first product given trivially generalises but the second doesn't, it only works as described in 2D. So in higher dimensions its not clear if this product is defined or if there are other maybe multiple products which simplify to this in 2D.--<small>[[User:JohnBlackburne|JohnBlackburne]]</small><sup>[[User_talk:JohnBlackburne|words]]</sup><sub style="margin-left:-2.0ex;">[[Special:Contributions/JohnBlackburne|deeds]]</sub> 21:05, 1 September 2010 (UTC)
****Oh ok, I thought you referred to it being 2x2, not being bidimensional. --[[User:Cyclopia|<
** The definition is a bit of a tautology, and the sources were probably assuming readers would fill in the gaps. I'm thinking [http://books.google.com/books?id=Un_15Im3NhUC&pg=PA31#v=onepage&f=false] probably covers the subject enough to establish notability. The article doesn't list any sources though, and it's unclear to me how much of the material should be removed. The definition alone isn't enough to justify the existence of the article.--[[User:RDBury|RDBury]] ([[User talk:RDBury|talk]]) 20:16, 31 August 2010 (UTC)
*** There is definitely material that can bring the article beyond a mere definition: e.g. here it is an article [http://books.google.com/books?hl=en&lr=&id=HuSqsKIzTSYC&oi=fnd&pg=PA19&dq=%22quaternionic+matrix%22&ots=lYRkWSoKRR&sig=rTC7e_rXQpq1tgSjinS1dhHGAbE#v=onepage&q=%22quaternionic%20matrix%22&f=false on eigenvalues of a quaternionic matrix]. I am unfortunately far from having the mathematical competence to properly do that, I'm going to notify the appropriate Wikiproject. --[[User:Cyclopia|<
* '''comment''' The determinant and therefore the eignenvalue problem are where you're going to have problems with such matrices. When calculating the determinant of a real or complex matrix you can do so in a variety of ways with order of multiplication usually ignored, but order matters when multiplying quaternions. A lot of the sources seem to be concerned with this problem, but more as something they're all trying to address, perhaps in different ways, rather than a known definition they can all agree on so which we can be pretty sure of.--<small>[[User:JohnBlackburne|JohnBlackburne]]</small><sup>[[User_talk:JohnBlackburne|words]]</sup><sub style="margin-left:-2.0ex;">[[Special:Contributions/JohnBlackburne|deeds]]</sub> 21:05, 1 September 2010 (UTC)
** Which is, if anything, a reason more to keep this article, not to delete it. It seems a lively topic in mathematics. --[[User:Cyclopia|<
*'''comment''' We need definitions and results we can use for the article, which I don't see in any of the sources which all seem recent. It's not the place of Wikipedia to try and summarise ongoing, maybe even contentious, results. [http://www.jstor.org/pss/20488503 this] looks more promising but I can't read beyond the first page.--<small>[[User:JohnBlackburne|JohnBlackburne]]</small><sup>[[User_talk:JohnBlackburne|words]]</sup><sub style="margin-left:-2.0ex;">[[Special:Contributions/JohnBlackburne|deeds]]</sub> 23:19, 1 September 2010 (UTC)
::*Well, no, Wikipedia is the correct place to report what RS (in this case, academic papers and books) report on a subject, regardless of its ongoing status and controversiality. --[[User:Cyclopia|<
* '''Delete'''. Quaternionic matrices, i.e. square matrices whose elements are quaternions, are well-known and useful objects — for example, the compact [[symplectic group]] is realized as the maximal compact subgroup of ''GL''(''n'','''H'''). However, we already have an article [[matrix ring]] which deals with matrices over an arbitrary associative ring and I simply do not see the need for duplicating the same material in the special case of quaternions. On the other hand, the so-called "Hamiltonian" and "Octonionic" products, whose description at present comprises all of the article under discussion, are non-standard and possibly OR. (It is hard to be certain and it would be difficult to sort out notability issues because, historically, quaternionists have behaved as a sect, with their own societies and journals, and the fruits of their studies are quite isolated from mainstream mathematics.) [[User:Arcfrk|Arcfrk]] ([[User talk:Arcfrk|talk]]) 04:07, 2 September 2010 (UTC)
::Thanks for the insightful comment. However I see in the literature many articles specifically dealing with quaternionic matrices, while the [[matrix ring]] article does not cite the special case of quaternionic matrices at all. It doesn't talk about eigenvalues, too, while there seems to be substantial literature about the problem of defining the eigenvalue of a quaternionic matrix. The article needs OR to be hashed out, but even if it is a special case, it seems a sourced one and therefore [[WP:GNG|notable]]. --[[User:Cyclopia|<
::Quaternionic matrices seem to have specific application in quantum mechanics that wouldn't be captured in a more generic article. Also, I don't think we should assume that everyone who might be interested in this is going to be familiar with more abstract ideas such as associated algebras.--[[User:RDBury|RDBury]] ([[User talk:RDBury|talk]]) 15:32, 2 September 2010 (UTC)
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::: Well, there are also many articles in the literature dealing with rational matrices, real matrices, and complex matrices, but would that be a sufficient reason to create articles "Rational matrix", "Real matrix" and "Complex matrix"? The argument about quantum mechanics seems equally spurious to me: if there is no mathematical theory underlying this ostensible application (with which I am not familiar) then it should be described within its natural context, i.e. in the article on whatever quantum mechanical phenomenon it is relevant to. [[User:Arcfrk|Arcfrk]] ([[User talk:Arcfrk|talk]]) 02:04, 3 September 2010 (UTC)
:::: As long as there is a specific literature on the subject, I would say yes. We have [[integer matrix]], and [[complex matrix]] seems a reasonable article to me, given some of the [http://scholar.google.com/scholar?q=%22complex+matrix%22 literature results] deal with specific algorithms about them. Make no mistake: even if I'm no expert I understand there can be reasons for a merge, but given that the current matrix ring article doesn't contain anything on the notable subcases, I'd keep the article for now and then work on a merge, rather than bluntly deleting it -the latter outcome does a disservice to readers. --[[User:Cyclopia|<
* '''Comment''' The so-called "Hamiltonian" product is simply the usual associative product of matrix multiplication. If an ''n''×''n'' quaternionic matrix is represented using a 2''n'' × 2''n'' complex matrix or a 4''n'' × 4''n'' real matrix with particular structure, the product of the two quaternionic matrices on this definition properly matches up with the corresponding usual matrix product of the complex matrices or real matrices representing it. I am not sure about the meaning of a quaternionic determinant, and how it would relate to the corresponding determinants of the corresponding complex or the real matrices, but this is something that the article could usefully discuss. We have articles on various forms of matrices with particular types of structure, so I don't see an objection to an article on these matrices, if there is something interesting to say about them.
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::I took a stab at getting the article to at least the stub level of quality. This was based on a single reference so I'm pretty sure more could be added.--[[User:RDBury|RDBury]] ([[User talk:RDBury|talk]]) 17:18, 2 September 2010 (UTC)
::: Sorry, but that just kicks the can down the road, because all it does is create a quaternionic content fork for [[Matrix ring]]. In my opinion (also expressed at the talk page), it would be far better to add the relevant material there directly and to delete or redirect the page under discussion. [[User:Arcfrk|Arcfrk]] ([[User talk:Arcfrk|talk]]) 02:04, 3 September 2010 (UTC)
::::I wouldn't have bothered if there was only general material here. But I think the material on determinants is sufficiently specific that the article is not a content fork. Also, I think there is a case for having a version for people who are not familiar with abstract algebra since it appears that the applications are in physics.--[[User:RDBury|RDBury]] ([[User talk:RDBury|talk]]) 08:20, 6 September 2010 (UTC)
::::[[Matrix ring]] only deals with square matrices. --[[User talk:Lambiam|Lambiam]] 20:06, 8 September 2010 (UTC)
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:<span style="color:#FF4F00;">'''[[WP:RELIST|Relisted]] to generate a more thorough discussion so consensus may be reached.'''</span><br /><small>Please add new comments below this notice. Thanks, [[User:JForget|<span style="color:orange;">'''JForget''' </span>]] 00:48, 7 September 2010 (UTC)</small><!-- from Template:Relist -->
*<small class="delsort-notice">'''Note''': This debate has been included in the [[Wikipedia:WikiProject Deletion sorting/Science|list of Science-related deletion discussions]]. <!--Template:Deletion sorting--></small> <small>-- [[User:Gene93k|• Gene93k]] ([[User talk:Gene93k|talk]]) 17:27, 7 September 2010 (UTC)</small>
*'''Keep''' Finding a source for this seems easy, e.g. ''[http://books.google.com/books?id=ybQrAAAAYAAJ Quaternionic and Clifford calculus for physicists and engineers]'', which has a section specifically about this notion. Please see [[WP:BEFORE]]. [[User:Colonel Warden|Colonel Warden]] ([[User talk:Colonel Warden|talk]]) 08:49, 8 September 2010 (UTC)
*'''Keep''', has enough references in its present state to establish notability; also, the material in the section Determinants is specific to quaternionic matrices and cannot be reduced to the case of matrices over a ring. --[[User talk:Lambiam|Lambiam]] 16:12, 8 September 2010 (UTC)
*'''comment''' I'm not sure I can change my !vote as I didn't !vote but it now looks fine to me: the results make sense, seem properly sourced (I can't check myself as they all seem behind paywalls or Google's limits on what I can view) and make for a coherent if short article.--<small>[[User:JohnBlackburne|JohnBlackburne]]</small><sup>[[User_talk:JohnBlackburne|words]]</sup><sub style="margin-left:-2.0ex;">[[Special:Contributions/JohnBlackburne|deeds]]</sub> 16:32, 8 September 2010 (UTC)
:''The above discussion is preserved as an archive of the debate. <span style="color:red">'''Please do not modify it.'''</span> Subsequent comments should be made on the appropriate discussion page (such as the article's talk page or in a [[Wikipedia:Deletion review|deletion review]]). No further edits should be made to this page.'' <!--Template:Afd bottom--></div>
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