Wikipedia:Articles for deletion/Quaternionic matrix: Difference between revisions

Revision as of 07:53, 2 September 2010

Revision as of 09:06, 2 September 2010

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* '''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|<font color="green">Cycl</font><big>o</big><font color="green">pia</font>]][[User talk:Cyclopia|<font color="red">^talk</font>]] 07:53, 2 September 2010 (UTC)

* '''Comment''' The so-called "Hamiltonian" product is simply the usual associative product of matrix multiplication. If an ''n''&times;''n'' quaternionic matrix is represented using a 2''n''&times2''n'' complex matrix or a 4''n'' &times; 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.

:The motivation for the "Octonian" product is less apparent to me, and it could do with some sourcing. Possibly it is interesting and useful, but there seem to be no easily found references to it that jump out, at least at a surface level; and, perhaps I'm missing something, but I don't see an obvious connection between this product and the Octonian product of a pair of quaternions defined by the Cayley-Dickson construction. So this at the very least needs some clarification. [[User:Jheald|Jheald]] ([[User talk:Jheald|talk]]) 09:06, 2 September 2010 (UTC)