A class of oscillatory matrices with exponent \(n - 1\)
type: Item
instance of: scholarly article
title: A class of oscillatory matrices with exponent \(n - 1\)
zbMATH Open document ID: 1122.15010
published in: Linear Algebra and its Applications
publication date: 2007-06-26T00:00:00Z
review text: The authors describe the class of \(n\times n\) oscillatory matrices which have maximal exponent equal to \(n-1\). \textit{F. P. Gantmacher} and \textit{M. G. Krein} [Oscillation matrices and kernels and small vibrations of mechanical systems. (2002; Zbl 1002.74002)] laid the groundwork for the theory of oscillatory matrices. They proved that the eigenvalues of an oscillatory matrix are real, positive, and distinct. In the paper of \textit{S. M. Fallat, M. Fiedler} and \textit{T. L. Markham} [Linear Algebra Appl. 359, No.~1--3, 79--90 (2003; Zbl 1026.15008)] a question was raised about describing the \(n\times n\) oscillatory matrices whose exponent is equal to \(n-1\). This class is completely characterized in this paper.
reviewed by: Yueh-er Kuo
Mathematics Subject Classification ID: 15A15
Mathematics Subject Classification ID: 15B48
zbMATH DE Number: 5167490
zbMATH Keywords: totally positive and nonnegative matrices
zbMATH Keywords: oscillatory matrices
zbMATH Keywords: bidiagonal factorization
zbMATH Keywords: exponent
author: Shaun M. Fallat
author: Xiaoping Liu
MaRDI profile type: Publication
full work available at URL: j.laa.2007.02.023
OpenAlex ID: W1966982704
cites work: Totally positive matrices
cites work: Combinatorics and total positivity
cites work: Some properties of totally positive matrices
cites work: Bidiagonal Factorizations of Totally Nonnegative Matrices
cites work: A remark on oscillatory matrices
cites work: Generalized oscillatory matrices
cites work: Generalized totally positive matrices
cites work: Generalized totally nonnegative matrices
cites work: Total positivity: tests and parametrizations.
cites work: Q4552277
cites work: Q4375491
cites work: Q4381523
cites work: Q5624248
cites work: On the boundary of totally positive upper triangular matrices
DOI: 10.1016/J.LAA.2007.02.023
description: scientific article; zbMATH DE number 5167490