Small polynomial matrix presentations of nonnegative matrices
type: Item
instance of: scholarly article
title: Small polynomial matrix presentations of nonnegative matrices
zbMATH Open document ID: 1026.15015
DOI: 10.1016/S0024-3795(02)00313-0
author: Mike Boyle
author: Douglas Lind
published in: Linear Algebra and its Applications
publication date: 2003-02-05T00:00:00Z
review text: Matrices whose entries are polynomials with nonnegative coefficients are used from some time ago to represent nonnegative matrices. Their use has special interest in the problem of determining the minimum size polynomial matrix presenting a prescribed nonzero spectrum. In this paper the authors construct polynomial matrices of small size presenting nonnegative matrices with certain spectral and algebraic constraints. They show how certain geometrical ideas interact with polynomial matrices.
Mathematics Subject Classification ID: 15B48
Mathematics Subject Classification ID: 15A54
Mathematics Subject Classification ID: 15A29
zbMATH DE Number: 1864733
zbMATH Keywords: nonnegative matrices
zbMATH Keywords: polynomial matrices
zbMATH Keywords: inverse spectral problem
reviewed by: M. Gasca
MaRDI profile type: Publication
cites work: Linear Transformations with Invariant Cones
cites work: Q4326384
cites work: Q3893024
cites work: Q4281308
cites work: Q4427623
cites work: The spectra of nonnegative matrices via symbolic dynamics
cites work: Algebraic Shift Equivalence and Primitive Matrices
cites work: Resolving maps and the dimension group for shifts of finite type
cites work: Q4037008
cites work: Row Stochastic Matrices Similar to Doubly Stochastic Matrices
cites work: The real and the symmetric nonnegative inverse eigenvalue problems are different
cites work: The spectra of nonnegative integer matrices via formal power series
cites work: Characterization of inert actions on periodic points. Part I
cites work: Q4527109
cites work: A characterization of trace zero nonnegative \(5\times 5\) matrices
cites work: The entropies of topological Markov shifts and a related class of algebraic integers
cites work: The spectra of topological Markov shifts
cites work: An Introduction to Symbolic Dynamics and Coding
cites work: A note on an inverse problem for nonnegative matrices
cites work: Q4039989
cites work: On positive matrices
cites work: Q5638112
cites work: A Mathematical Theory of Communication
full work available at URL: s0024-3795(02)00313-0
OpenAlex ID: W2106122951
description: scientific article; zbMATH DE number 1864733