We assume that $n \geqslant 3$. Let $u$ be an endomorphism of $E$ nilpotent of index 2 and of rank $r$. Show that $\operatorname{Im} u \subset \operatorname{Ker} u$ and that $2r \leqslant n$.
We assume that $n \geqslant 3$. Let $u$ be an endomorphism of $E$ nilpotent of index 2 and of rank $r$.
Show that $\operatorname{Im} u \subset \operatorname{Ker} u$ and that $2r \leqslant n$.