\begin{definition}[Definition:Irreducible (Representation Theory)/Linear Representation]
Let $\rho: G \to \GL V$ 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:
: $\forall g \in G: \map {\map \rho g} W \subseteq W$
Category:Definitions/Representation Theory
\end{definition}