The upper bound for the index of nilpotency for a matrix commuting with a given nilpotent matrix
Polona Oblak · Linear and Multilinear Algebra · 2008
We study the set () of all possible Jordan canonical forms of nilpotent matrices commuting with a given nilpotent matrix B. We describe () in the special case when B has only one Jordan block and discuss some consequences. 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.