Definition:Equivalent Linear Representations

Definition
Let $ \struct {G, \cdot}$ be a group.

Consider two linear representations $\rho: G \to \GL V$ and $\rho': G \to \GL W$ of $G$.

Then $\rho$ and $\rho'$ are called equivalent (linear representations) their correspondent $G$-modules using Correspondence between Linear Group Actions and Linear Representations are isomorphic.