The upper bound for the index of nilpotency for a matrix commuting with a given nilpotent matrix

2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/143188We study the set $\partition{\nb}$ of all possible Jordan canonical forms of nilpotent matrices commuting with a given nilpotent matrix $B$. We describe $\partition{\nb}$ in the special case when $B$ has only one Jordan block. In the general case, we find the maximal possible index of nilpotency in the set of all nilpotent matrices commuting with a given nilpotent matrix. We consider several examples.17 pagesCommutative Algebra15A04, 15A21, 15A27The upper bound for the index of nilpotency for a matrix commuting with a given nilpotent matrixtext