Corollary

The orthogonal of the image $u(E)$ in $F^*$ is the kernel $^t u^{-1}(0)$ of $^t u$.

The orthogonal of E in $E^*$ is 0.

If $u : E \to F$ is an isomorphism, $^t u : F^* \to E^*$ is an isomorphism and if $v : F \to E$ is the inverse isomorphism of $u$, $^t v$ is the inverse isomorphism of $^t u$ (formulae (17) and (18)).