We assume that $n = 2$. Let $u$ be an endomorphism of $E$ nilpotent of index $p \geqslant 2$. Show that there exists a vector $x$ in $E$ such that $u^{p-1}(x) \neq 0$.
We assume that $n = 2$. Let $u$ be an endomorphism of $E$ nilpotent of index $p \geqslant 2$.
Show that there exists a vector $x$ in $E$ such that $u^{p-1}(x) \neq 0$.