# Definition:Equivalent Linear Representations

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) if and only if their correspondent $G$-modules using Correspondence between Linear Group Actions and Linear Representations are isomorphic.