\begin{definition}[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)''' {{iff}} their correspondent $G$-modules using Correspondence between Linear Group Actions and Linear Representations are isomorphic.
{{rewrite|above line needs rewriting, but I can't come up with a suitable replacement}}
{{explain|The "isomorphic" link goes to a generic "abstract algebra" page, but I believe no actual definition has been made for an isomorphism between two G-modules.}}
Category:Definitions/Representation Theory
\end{definition}