Definition:Faithful Linear Representation of Group

Let $(k,+,\circ)$ 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 $(G, \cdot)$ be a finite group.

Let $\rho : G \to GL(V)$ be a linear representation of $G$ on $V$.

We say that $\rho$ is faithful if the kernel of $\rho$ is trivial.