Locally finite operator
Appearance
In mathematics, a linear operator is called locally finite if the space is the union of a family of finite-dimensional -invariant subspaces.
In other words, there exists a family of linear subspaces of , such that we have the following:
- each is finite-dimensional.
Examples
- any linear operator on a finite-dimensional space is trivially locally finite
- any diagonalizable (i.e. there exists a basis of whose elements are all eigenvectors of ) linear operator is locally finite, because it is the union of subspaces spanned by finitely many eigenvectors of .