Formula for curvature of dual connection

Statement

Suppose $M$ is a differential manifold, $E$ is a vector bundle over $M$ , and $\nabla$ is a connection on $E$ . Suppose $E^{*}$ is the dual bundle and $\nabla ^{*}$ is the dual connection to $\nabla$ . If $R_{\nabla }$ and $R_{\nabla ^{*}}$ denote respectively the Riemann curvature tensors of $\nabla$ and $\nabla ^{*}$ , then we have:

$R_{\nabla ^{*}}(l)=s\mapsto -l(R(X,Y)(s))$ .