Addition_of_Linear_Transformations

Let $\left({G, +_G, \circ}\right)_R$ and $\left({H, +_H, \circ}\right)_R$ be $R$-modules. Let $\phi: G \to H$ and $\psi: G \to H$ be linear transformations. Let $\phi +_H \psi$ be the operation on $H^G$ induced by $+_H$ as defined in Induced Structure. Then $\phi +_H \psi: G \to H$ is a linear transformation.