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