Wikipedia:Articles for deletion/Quaternionic matrix

Quaternionic matrix

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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. JohnBlackburne^words_deeds 11:18, 31 August 2010 (UTC)[reply]

Keep: A trivial 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). --Cyclopia ^talk 18:10, 31 August 2010 (UTC)[reply]
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). A search on both "Hamiltonian product" and "quaternionic matrix" turns up only mirrors of this page and 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.--JohnBlackburne^words_deeds 19:07, 31 August 2010 (UTC)[reply]
- I don't understand where did you get the impression that the article is only on 2x2 matrices. --Cyclopia^talk 19:41, 1 September 2010 (UTC)[reply]
  - 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.--JohnBlackburne^words_deeds 21:05, 1 September 2010 (UTC)[reply]
    - Oh ok, I thought you referred to it being 2x2, not being bidimensional. --Cyclopia ^talk 22:48, 1 September 2010 (UTC)[reply]

- The definition is a bit of a tautology, and the sources were probably assuming readers would fill in the gaps. I'm thinking [1] 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.--RDBury (talk) 20:16, 31 August 2010 (UTC)[reply]
  - There is definitely material that can bring the article beyond a mere definition: e.g. here it is an article 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. --Cyclopia ^talk 19:40, 1 September 2010 (UTC)[reply]
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.--JohnBlackburne^words_deeds 21:05, 1 September 2010 (UTC)[reply]
- Which is, if anything, a reason more to keep this article, not to delete it. It seems a lively topic in mathematics. --Cyclopia ^talk 22:48, 1 September 2010 (UTC)[reply]
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. this looks more promising but I can't read beyond the first page.--JohnBlackburne^words_deeds 23:19, 1 September 2010 (UTC)[reply]

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. --Cyclopia ^talk 23:34, 1 September 2010 (UTC)[reply]