Let $(E , \omega)$ be a symplectic vector space of dimension $n = 2m$ and let $u \in \operatorname { Symp } _ { \omega } ( E )$ be a symplectic endomorphism of $E$. Let $e _ { 1 } \in E$ be a non-zero vector. Justify the existence of $f _ { 1 } \in E$, not collinear with $e _ { 1 }$, such that $\omega \left( e _ { 1 } , f _ { 1 } \right) = 1$.