Talk:Kernel (mathematics)

message: The introduction now reads: "In mathematics, especially abstract algebra, a kernel is a general construction which measures the failure of a homomorphism or function to be injective."
Given the meaning of "kernel" in integral calculus it seems to me that either (1) this introduction would be better (not good, merely better): "In mathematics, the term "kernel" has multiple meanings. In abstract algebra, a kernel is a general construction which measures the failure of a homomorphism or function to be injective.", or (2) the relationship among the different meanings should be outlined.
Harold f 06:39, 31 December 2006 (UTC)
thread_title: "Kernel" defined in more ways than intro suggests?

message: This page should be converted into a disambiguation page. There is a common meaning of kernel in abstract algebra, linear algebra, and category theory (though not in the sense of "equalizer"). The usage of kernels in set theory, and for equalizers, seems rather rare to me, and the alternative meanings in integral operators and statistics are completely different. Geometry guy 01:26, 1 June 2007 (UTC)
thread_title: Convert to dab

message: Should kernel (mathematics) become a disambig page?  There was a complaint that the main usage is 4th on the list (a few pages down).  If this was a disambig age, being fourth would not be a problem.  Also in my experience (at a PDE heavy institution) the main usage of kernel is the one from integral operators, such as a heat kernel or green's function.
Once we have a sane disambiguation page (either Kernel (disambiguation) or Kernel (mathematics)), then we should probably go through the kernel articles and make sure appropriate links are made.  I've added some links to kernel (algebra), but it is missing kernel (category theory) and probably others (hard to tell, since I think the disambig page is also missing some, and certainly kernel (mathematics) is missing many). JackSchmidt (talk) 16:28, 20 June 2008 (UTC)
replies: text: I think it would be preferrable to have one good article covering all the meanings of kernel related to f(x)=0. The only article which presents substantial additional material is kernel (matrix), parts of which (such as numerical calculations) could be summarized in this article. The terrible amount of redundancy could be amended if material from sections like Kernel (algebra)#Ring homomorphisms would be moved to ring homomorphism, in this case (which, by the way, also already contains material on the kernel). Similarly, all instances of "X/ker (f) \cong im(f)" should be centered in Isomorphism theorem and so on. Jakob.scholbach (talk) 16:47, 20 June 2008 (UTC)
replies: text: This seems reasonable, and would cut down on the confusion of analytic kernels versus algebraic kernels.  Should the other algebraic kernel articles redirect to sections of the one true algebraic kernel, or to their associated homomorphism pages? JackSchmidt (talk) 18:07, 20 June 2008 (UTC)
replies: text: Another question is what to do with the (related) category theory and set theory/universal algebra definitions. Since both are quite abstract it might be best to keep them separate, e.g. kernel (algebra), kernel (category theory), kernel (equivalence relation). --Hans Adler (talk) 18:14, 20 June 2008 (UTC)

text: Changed into DAB, and replaced wording that would be incomprehensible to anyone but a specialist (that belongs to the individual pages, if anywhere) by something that may not be so exact but is hopefully understandable. About a year ago I have moved several nullspace articles into kernel articles, but I have stopped short of such radical cut at that time. Jmath666 (talk) 05:10, 27 June 2008 (UTC)
thread_title:  Kernel cleanup (copied from [[Wikipedia talk:WikiProject Mathematics]]) 

message: Following discussion on Talk:Kernel, I've replaced the Mathematics section with a single entry pointing here. There were three entries there not on this page, but I'm not certain where they ought to go or even if they all ought to be included.
* Polygon kernel
* Kernel smoother
* Cooperative game#The kernel
CarrieVS (talk) 07:55, 7 June 2012 (UTC)
thread_title:  Entries from Kernel