Definition:Irreducible (Representation Theory)/Linear Representation

Definition
Let $\rho: G \to \operatorname{GL} \left({V}\right)$ be a linear representation.

Then $\rho$ is irreducible iff it is not reducible.

That is, iff there exists no non-trivial proper vector subspace $W$ of $V$ such that:
 * $\forall g \in G: \rho \left({g}\right) \left({W}\right) \subseteq W$