Direct sum of connections

Definition

Suppose $M$ is a differential manifold and $E,E'$ are vector bundles on $M$. Suppose $\nabla ,\nabla '$ are connections on $E$ and $E'$ respectively. Then, we define $\nabla \oplus \nabla '$ as a connection on $E\oplus E'$ given by:

$(\nabla \oplus \nabla ')(s,s')=\nabla (s)\oplus \nabla '(s')$.