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Mathematics  2007 

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

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Abstract:

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.

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