We assume that $f$ is a nilpotent endomorphism of $E$. We denote by $r$ the smallest natural integer such that $f^r = 0$. Show that $f$ is cyclic if and only if $r = n$. Specify the companion matrix.
We assume that $f$ is a nilpotent endomorphism of $E$. We denote by $r$ the smallest natural integer such that $f^r = 0$. Show that $f$ is cyclic if and only if $r = n$. Specify the companion matrix.