Let $V \in \mathcal{M}_n(\mathbb{C})$ be a nilpotent matrix of index $p$. We propose to study the equation $R^2 = V$. Show that, if $2p - 1 > n$, then there is no solution.
Let $V \in \mathcal{M}_n(\mathbb{C})$ be a nilpotent matrix of index $p$. We propose to study the equation $R^2 = V$.
Show that, if $2p - 1 > n$, then there is no solution.