\begin{definition}[Definition:Linear Representation/Group]
Let $\struct {K, +, \circ}$ be a field.
Let $V$ be a vector space over $K$ of finite dimension.
Let $\GL V$ be the general linear group of $V$.
Let $\struct {G, \cdot}$ be a finite group.
A '''linear representation of $G$ on $V$''' is a group homomorphism $\rho: G \to \GL V$.
\end{definition}