The upper bound for the index of nilpotency for a matrix commuting with a given nilpotent matrix
Oblak, Polona, 1978-
We study the set ▫${\mathcal{P(N}}_B)$▫ of all possible Jordan canonical forms of nilpotent matrices commuting with a given nilpotent matrix ▫$B$▫. We describe ▫${\mathcal{P(N}}_B)$▫ 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.
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