Curvature matrix of a connection

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Definition

Suppose M is a differential manifold, E a vector bundle over M, and \nabla a connection over M. Let p \in M and U \ni p be an open set such that the vector bundle E, restricted to U, is trivial. The curvature matrix of p, denoted \Omega(p) is defined by:

\Omega = d\omega + \omega \wedge \omega