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

Revision as of 09:06, 2 September 2010

Revision as of 09:07, 2 September 2010

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::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'' &times2times; 2''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)