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{{unreferenced|date=November 2012}}

In [[mathematics]], a [[linear operator]] <math>f: V\to V</math> is called '''locally finite''' if the [[linear space|space]] <math>V</math> is the union of a family of finite-dimensional <math>f</math>-[[invariant subspace]]s.

In other words, there exists a family <math>\{ V_i\vert i\in I\}</math> of linear subspaces of <math>V</math>, such that we have the following:
* <math>\bigcup_{i\in I} V_i=V</math>
* <math>(\forall i\in I) f[V_i]\subseteq V_i</math>
* Each <math>V_i</math> is finite-dimensional.

==Examples==
* Every linear operator on a finite-dimensional space is trivially locally finite.
* Every [[diagonalizable]] (i.e. there exists a [[basis]] of <math>V</math> whose elements are all [[eigenvector]]s of <math>f</math>) linear operator is locally finite, because it is the union of subspaces spanned by finitely many eigenvectors of <math>f</math>.

{{linear-algebra-stub}}

[[Category:Abstract algebra]]
[[Category:Functions and mappings]]
[[Category:Linear algebra]]
[[Category:Transformation (function)]]

Plebanski tensor - Revision history

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