Category talk:Linear operators

Many missing articles
This seems an absurdly general category, and many articles appear to be missing from it. I suppose the most obvious are:
 * Linear map
 * Matrix
 * Linear functional

Beyond that, even if we restrict attention just to operators on functions, there are a huge number of articles that have been omitted. Any integral transform fits the bill:
 * Fourier transform
 * Hilbert transform
 * Integral transform
 * Laplace transform
 * Laplace-Stieltjes transform
 * Newtonian potential
 * Penrose transform
 * Radon transform
 * Riemann-Liouville integral
 * Riesz potential
 * Riesz transform
 * Stieltjes transformation
 * X-ray transform

Also, many differential operators are of this kind, including
 * covariant derivative
 * differential operator (the article is mostly about the linear theory)
 * elliptic complex
 * elliptic differential operator
 * exterior derivative
 * Hessian matrix
 * pseudo-differential operator
 * ultrahyperbolic operator

Pretty much any operator that generalizes the derivative:
 * Curl (mathematics)
 * derivation (abstract algebra)
 * Derivative (generalizations)
 * difference operator
 * Directional derivative
 * Divergence
 * Frechet derivative
 * Gateaux derivative
 * Gradient
 * Jacobian derivative
 * Lie derivative
 * Partial derivative
 * variational derivative
 * weak derivative

And so forth. Personally, I think such a category is a hopeless endeavor. A sizeable portion of modern mathematics is dedicated to the study of linear operators, and so attempting to put them all in such a category is a Sisyphean task. But if we are going to have a category at all, then we should at least endeavor to make it as complete as possible. Sławomir Biały (talk) 15:44, 8 June 2009 (UTC)


 * Maybe this category should have some subcategories (as Category:Functional analysis, for instance)? Boris Tsirelson (talk) 18:43, 8 June 2009 (UTC)


 * That's a good idea. Some of the current occupants could come in via Category:Generalizations of the derivative and Category:Integral transforms.  Sławomir Biały (talk) 07:04, 9 June 2009 (UTC)

General categories have their place, even if everything in them should be in a subcategory. Articles in a subcategory are not "missing". It seems this category probably has an organisational role to play. Probably an effort should be made to put everything into at least one subcategory: this is a good way to notice subcategories that should be created becuse they are useful. Charles Matthews (talk) 12:58, 9 June 2009 (UTC)


 * Yes, I understand that. Prior to this morning, however, you may note that the articles were missing in any sense of the word as there were no subcategories at all.  Since then, I have been busily attempting to implement Boris's suggestion.  I agree that we should attempt to keep things in subcategories as much as possible.  Sławomir Biały (talk) 15:32, 9 June 2009 (UTC)

By the way, what about Unbounded operator (and some links therefrom)? Boris Tsirelson (talk) 13:08, 9 June 2009 (UTC) Maybe also Discontinuous linear map. Boris Tsirelson (talk) 06:10, 13 June 2009 (UTC)