Isomorphic representations

Representations $\rho :G\to \mathrm{GL}(V)$ and ${\rho }^{\prime }:G\to \mathrm{GL}(V^{\prime })$ are isomorphic when an invertible linear map $T:V\to V^{\prime }$ intertwines the actions: $T\rho (g)={\rho }^{\prime }(g)T$ for every $g\in G$.