Commuting Nilpotent Operators and Maximal Rank

ÖZTÜRK S.

COMPLEX ANALYSIS AND OPERATOR THEORY, vol.4, no.4, pp.901-904, 2010 (SCI-Expanded, Scopus) identifier identifier

  • Publication Type: Article / Article
  • Volume: 4 Issue: 4
  • Publication Date: 2010
  • Doi Number: 10.1007/s11785-009-0029-x
  • Journal Name: COMPLEX ANALYSIS AND OPERATOR THEORY
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.901-904
  • Middle East Technical University Affiliated: Yes

Abstract

Let X, (X) over tilde 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 - (X) over tilde is a certain linear combination of products of pairwise commuting nilpotent matrices, then X is of maximal rank if and only if (X) over tilde is of maximal rank.