Character of direct sum of linear representations is sum of characters

Statement
 Suppose $$G$$ is a group, $$K$$ is a field, and $$\rho_1:G \to GL(V_1), \rho_2:G \to GL(V_2)$$ are finite-dimensional linear representations of $$G$$ over $$K$$. Denote by $$\chi_{\rho_1}, \chi_{\rho_2}$$ the characters of the representations $$\rho_1,\rho_2$$ respectively. Denote by $$\rho_1 \oplus \rho_2$$ the direct sum of linear representations $$\rho_1,\rho_2$$ and by $$\chi_{\rho_1 \oplus \rho_2}$$ its character. Then, we have the following for any $$g \in G$$:

$$\chi_{\rho_1 \oplus \rho_2} = \chi_{\rho_1}(g) + \chi_{\rho_2}(g)$$

Recall that the character of a linear representation is the function that sends any $$g$$ to the trace of the corresponding linear map.

Related facts

 * Character of tensor product of linear representations is product of characters