%0 Journal Article
%T The upper bound for the index of nilpotency for a matrix commuting with a given nilpotent matrix
%A Polona Oblak
%J Mathematics
%D 2007
%I arXiv
%X We 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.
%U http://arxiv.org/abs/math/0701561v2