Definition:Equivalent Linear Representations

Definition
Let $(G,\cdot)$ be a group and consider two representations $\rho:G\to \operatorname{GL}\left({V}\right)$ and $\rho^\prime:G\to \operatorname{GL}\left({W}\right)$

We say that $\rho$ and $\rho^\prime$ are equivalent iff their correspondent $G$-modules using Equivalence of Representation Definitions are isomorphic