\begin{definition}[Definition:Faithful Linear Representation of 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.
Let $\rho : G \to \GL V$ be a linear representation of $G$ on $V$.
Then $\rho$ is '''faithful''' {{iff}} the kernel of $\rho$ is trivial.
Category:Definitions/Representation Theory
\end{definition}