Talk:Kernel (linear algebra)
|WikiProject Mathematics||(Rated Start-class, Mid-importance)|
|The content of Kernel (matrix) was merged into Kernel (linear algebra). That page now redirects here. For the contribution history and old versions of the redirected page, please see ; for the discussion at that location, see its talk page.|
Linear operator -> linear map
This article is about the kernel of a linear map. A linear map is called "linear operator" only in functional analysis, which is not the subject of this article. The problem lies in the fact that for most people and most WP articles using the concept of kernel, "linear map" is the standard name. I have encountered this problem by trying to disambiguate the links to kernel (mathematics) and finding that kernel (linear algebra) does not exists.
I propose to merge this article with Kernel (matrix). I think the reasons are quite obvious to anyone familiar with the subject. The two concepts are so intimately related it is often beneficial to conflate them (in the finite-dimensional case, that is) or treat a kernel of a matrix like a special case of a kernel of a linear map. I also expect sources to discuss one in conjunction with the other. Keφr (talk) 19:59, 26 November 2012 (UTC)
- Support: The kernel of a matrix is the kernel of the linear map it defines. In kernel (matrix), it is implicitly defined as such, even this is made explicit only later in the article. It seems that the editors of this article wanted to be more elementary by not talking of linear maps and vector spaces. IMO, this is silly, as the kernel is a vector space, and forgetting this remove any interest to the notion. Similarly, something that looks as a matrix without representing a linear map is not a matrix, but an two dimensional array. D.Lazard (talk) 08:08, 27 November 2012 (UTC)
- Support: for merging under this article's title, Kernel (linear algebra), rather than Kernel (matrix), since the former is the general concept, and the latter is merely a representation. — Quondum 09:43, 27 November 2012 (UTC)
- Support: there are only one concept (aside from integral kernel); therefore, there should be one article on it. -- Taku (talk) 11:15, 3 December 2012 (UTC)
- Performed by Keφr 11:19, 29 September 2013 (UTC) (Almost a year. Wow.)
I respond to the request to clean up the problem "Decide whether to explain this in terms of linear maps or matrices, or preferably organize the different views. Remove redundancies. Clean up markup. Do something with short sections."
- I cast the matrix A as a representation of the mapping. This should make clear that multiplication by a matrix over a vector field z is a representation of a linear map, not exhaustive of the class of linear maps.
- I changed "null space" to "kernel". If the article should instead use the term "null space", then perhaps the article title needs to be changed accordingly.
- I gathered all definitions of terms that were independent of a matrix representation and separated out those that were being discussed entirely in a matrix multiplication context.
- I refined the section now called “Illustration”.