Character of a linear representation

Definition in terms of linear representation as a homomorphism
Let $$G$$ be a group and $$\rho: G \to GL(V)$$ be a finite-dimensional linear representation over a field $$k$$. Then, the character of $$\rho$$ is the composite $$Tr \circ \rho$$ where $$Tr$$ is the trace map from $$GL(V)$$ to $$k$$.