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