# Invariant subspace for a linear representation

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This article gives a basic definition in the following area: linear representation theory

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## Definition

### Definition with symbols

Let be a group and be a linear representation of . An **invariant subspace** for is a linear subspace of such that for any , we have .

Given an invariant subspace of for , we can define a subrepresentation of on this invariant subspace (in fact, subrepresentations correspond to invariant subspaces. In other words, we can define an action of on be restricting the action on .