# Direct sum of connections

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