A bound on the exponent of a primitive matrix using Boolean rank
type: Item
instance of: scholarly article
title: A bound on the exponent of a primitive matrix using Boolean rank
zbMATH Open document ID: 0822.15005
DOI: 10.1016/0024-3795(92)00003-5
published in: Linear Algebra and its Applications
publication date: 1995-05-11T00:00:00Z
full work available at URL: http://purl.umn.edu/1876
review text: The authors prove that the exponent (also called index of primitivity) of a Boolean matrix of Boolean rank (also called Schein rank) \(b\) is at most \((b- 1)^ 2+ 2\), and that this bound can be attained for all dimensions \(n\) greater than \(b\).
Mathematics Subject Classification ID: 15B36
Mathematics Subject Classification ID: 15A45
Mathematics Subject Classification ID: 05B20
zbMATH DE Number: 754000
zbMATH Keywords: exponent
zbMATH Keywords: index of primitivity
zbMATH Keywords: Boolean matrix
zbMATH Keywords: Boolean rank
zbMATH Keywords: Schein rank
author: D. A. Gregory
author: S. J. Kirkland
author: Norman J. Pullman
reviewed by: Ki Hang Kim
MaRDI profile type: Publication
OpenAlex ID: W2037504144
cites work: Combinatorial matrix theory
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cites work: Q3758977
cites work: Generalizations of the spectral theorem for matrices. II. Matrix polynomials over arbitrary fields
cites work: Bounds on the exponent of primitivity which depend on the spectrum and the minimal polynomial
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cites work: Matrices permutation equivalent to primitive matrices
cites work: Unzerlegbare, nicht negative Matrizen
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description: scientific article; zbMATH DE number 754000