Let $u \in \operatorname{Symp}_\omega(E)$, $P = \operatorname{Vect}(e_1, f_1)$ with $\omega(e_1, f_1) = 1$, and $v = \delta \circ u$ where $\delta = \delta_2 \circ \delta_1$ satisfies $\delta(u(e_1)) = e_1$ and $\delta(u(f_1)) = f_1$. Show that $P$ is stable under $v$ and determine $v _ { P }$, the endomorphism induced by $v$ on $P$.