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)