Commuting Nilpotent Operators and Maximal Rank
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Abstract
Let X, \({\widetilde X}\) be commuting nilpotent matrices over k with nilpotency p t , where k is an algebraically closed field of positive characteristic p. We show that if \({X- \widetilde X}\) is a certain linear combination of products of pairwise commuting nilpotent matrices, then X is of maximal rank if and only if \({\widetilde X}\) is of maximal rank.
Keywords
Jordan canonical form Commuting nilpotent matricesMathematics Subject Classification (2000)
Primary 15A04 Secondary 15A21 15A33Preview
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