Potentially nilpotent sign pattern matrices
type: Item
instance of: scholarly article
title: Potentially nilpotent sign pattern matrices
zbMATH Open document ID: 0941.15012
DOI: 10.1016/S0024-3795(99)00163-9
author: Carolyn A. Eschenbach
author: Zhongshan Li
published in: Linear Algebra and its Applications
publication date: 2000-08-07T00:00:00Z
review text: The authors investigate the property \(N\) of being nilpotent. They establish several qualitative necessary conditions for patterns to allow \(N\) in Section 2 ``Qualitative conditions for nilpotence''. In Section 3 ``Patterns that allow nilpotence of index 2'', they investigate the sign patterns that allow nilpotence of index 2. In particular, they characterize minimum rank one patterns that allow nilpotence of index 2, and they provide several constructions of sign patterns that allow nilpotence of index 2. Section 4 ``The 3-by-3 sign patterns that allow \(N\)'' is devoted to characterize all 3-by-3 sign patterns that allow \(N\), and Section 5 ``\(C_r\)-cockades'' gives some results on \(C_r\)-cockade sign pattern matrices that allow \(N\) or preclude \(N\).
Mathematics Subject Classification ID: 15B33
zbMATH DE Number: 1399445
zbMATH Keywords: potentially nilpotent
zbMATH Keywords: sign pattern matrices
zbMATH Keywords: nilpotence of index 2
reviewed by: Yueh-er Kuo
MaRDI profile type: Publication
full work available at URL: s0024-3795(99)00163-9
OpenAlex ID: W1976642339
description: scientific article; zbMATH DE number 1399445