Curvature matrix of a connection

Definition

Suppose $M$ is a differential manifold, $E$ a vector bundle over $M$, and $\mathrm{\nabla }$ 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 $\mathrm{\Omega }(p)$ is defined by:

$\mathrm{\Omega }=d\omega +\omega \wedge \omega$