On the exponent of a primitive matrix containing a primitive submatrix
type: Item
instance of: scholarly article
title: On the exponent of a primitive matrix containing a primitive submatrix
zbMATH Open document ID: 0882.05037
DOI: 10.1016/S0024-3795(96)00401-6
published in: Linear Algebra and its Applications
publication date: 1997-08-05T00:00:00Z
review text: A square matrix \(A\) of order \(n\) with nonnegative entries is said to be primitive if \(A^m\) has all positive entries for some \(m\geq 1\). The smallest such \(m\) is called the exponent of \(A\). For a primitive matrix of order \(n+k\) having a primitive submatrix of order \(n\), it is shown that the exponent of \(A\) is at most \((n- 1)^2+ 2k+1\).
Mathematics Subject Classification ID: 05B20
Mathematics Subject Classification ID: 05C50
zbMATH DE Number: 1044254
zbMATH Keywords: Wielandt matrix
zbMATH Keywords: directed graph
zbMATH Keywords: exponent
zbMATH Keywords: primitive matrix
author: Leroy B. Beasley
author: S. J. Kirkland
reviewed by: D. Raghavarao
MaRDI profile type: Publication
cites work: Combinatorial matrix theory
cites work: The exponents of incidence matrices
cites work: On Powers of Non-Negative Matrices
cites work: A system of gaps in the exponent set of primitive matrices
cites work: A diameter bound on the exponent of a primitive directed graph
cites work: A bound on the exponent of primitivity in terms of diameter
cites work: Unzerlegbare, nicht negative Matrizen
full work available at URL: s0024-3795(96)00401-6
OpenAlex ID: W2197174231
description: scientific article; zbMATH DE number 1044254