Irreducible powerful ray pattern matrices
type: Item
instance of: scholarly article
title: Irreducible powerful ray pattern matrices
zbMATH Open document ID: 0994.15026
DOI: 10.1016/S0024-3795(01)00436-0
author: Zhongshan Li
author: Frank J. Hall
author: Jeffrey Stuart
published in: Linear Algebra and its Applications
publication date: 2002-05-15T00:00:00Z
full work available at URL: abstract.html
review text: A ray pattern is a matrix each of whose entries is either 0 or a ray in the complex plane originating from 0 (but not including 0). A ray pattern is a natural generalization of the concept of a sign pattern, whose entries are from the set \(\{+,-,0\}\). Powers of sign patterns and ray patterns, especially patterns whose powers are periodic, have been studied in several recent papers. A ray pattern \(A\) is said to be powerful if \(A^k\) is unambiguously defined for all positive integers \(k\). In this paper, irreducible powerful ray patterns, in particular, primitive powerful ray patterns, are completely characterized. Among the various characterizations, it is established that every irreducible powerful ray pattern is a ray multiple of a periodic irreducible powerful ray pattern.
Mathematics Subject Classification ID: 15B57
Mathematics Subject Classification ID: 15B48
Mathematics Subject Classification ID: 05B20
zbMATH DE Number: 1741559
zbMATH Keywords: Ray pattern matrix
zbMATH Keywords: sign pattern matrix
zbMATH Keywords: powerful ray pattern
zbMATH Keywords: unambiguously defined powers
reviewed by: Rodica Covaci
MaRDI profile type: Publication
cites work: Q4326384
cites work: Combinatorial matrix theory
cites work: From real to complex sign pattern matrices
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cites work: Reducible pattern \(k\)-potent ray pattern matrices
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description: scientific article; zbMATH DE number 1741559