We may study this linear operator in the context of functional analysis.
This characterization can be used to define the trace for a linear operator in general.
Let be a linear operator from to with and .
The most common kind of operator encountered are linear operators.
In a sense, the linear operators are not continuous because the space has "holes".
It makes sense to ask the analogous question about whether all linear operators on a given space are closed.
The key notion is that of a linear operator on a vector space.
Any closed linear operator defined on the whole space is bounded.
A short introduction to the perturbation theory of linear operators.
This article considers mainly linear operators, which are the most common type.