Let $V$ and $W$ be vector spaces. If $\phi: G\to GL(V)$ and $\psi:G\to GL(W)$ are two different representations of the group $G$, the direct sum $\phi \oplus \psi:G \to GL(V\oplus W)$ is also a representation of $G$ where $V\oplus W$ is given by the usual Cartesian product of vector spaces.
Wikidata ID: Q13582243