\begin{definition}[Definition:Reducible Linear Representation]
Let $\rho: G \to \GL V$ be a linear representation.
$\rho$ is '''reducible''' {{iff}} there exists a non-trivial proper vector subspace $W$ of $V$ such that:
:$\forall g \in G: \map {\map \rho g} W \subseteq W$
That is, such that $W$ is invariant for every linear operator in the set $\set {\map \rho g: g \in G}$.
\end{definition}