Acta mathematica scientia,Series A ›› 2011, Vol. 31 ›› Issue (3): 628-635.

• Articles • Previous Articles     Next Articles

The Potentially Nilpotent Sign Patterns in the Set of Sign Patterns FSP(3, n-3)

 LI Hong-Hai1, LI Jiong-Sheng2, SU Li1   

  1. 1.College of Mathematic and Information Science, |Jiangxi Normal University, Nanchang 330022; 2.Department of Mathematics,             |University of Science and Technology of China, Hefei |230026
  • Received:2009-07-08 Revised:2010-08-05 Online:2011-06-25 Published:2011-06-25
  • Supported by:

    国家自然科学基金(11026143)、江西省教育厅青年科学基金(GJJ09460)、江西师范大学青年成长基金(2711)和江西师范大学科研博士启动基金(Grant 2058)资助

Abstract:

A matrix A whose entries come from the set {+, -, 0} is called a sign pattern matrix, or sign pattern. If A is a sign pattern and A is a real matrix for which each entry has the same sign as the corresponding entry of A, then A is said to be a realization of A. A sign pattern is said to be potentially nilpotent if it has a nilpotent realization. In this paper, a class of sign patterns, denoted by FSP(3, n-3), is introduced. The authors determine all potentially nilpotent sign patterns in FSP(3, 4), and prove that no sign pattern of even order in  FSP(3, n-3) is potentially nilpotent.

Key words: Sign pattern matrix, Potentially nilpotent, Spectrally arbitrary

CLC Number: 

  • 05C50
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