Loewner and Bézout matrices
type: Item
instance of: scholarly article
title: Loewner and Bézout matrices
zbMATH Open document ID: 0644.15016
DOI: 10.1016/0024-3795(88)90151-6
author: Miroslav Fiedler
author: Vlastimil Pták
published in: Linear Algebra and its Applications
publication date: 1988-01-01T00:00:00Z
review text: Two recent papers of the authors [ibid. 86, 43-51 and 53-74 (1987; Zbl 0621.15015 and Zbl 0621.15016)] were devoted to the analysis of intertwining relations for Hankel and Bézout matrices. In the present paper the authors develop a parallel theory for the more complicated case of Loewner matrices. As byproducts a generalization of a recent result of \textit{Z. Vavrin} [ibid. 63, 227-236 (1984; Zbl 0558.15017)] on inverses of Loewner matrices as well as an interesting Barnett type formula for Loewnerians are obtained. In the final section an extension of the Barnett factorization formula for Bézout matrices B(f,g) to the case \(\deg (f)<size\) of matrix is presented.
Mathematics Subject Classification ID: 15B57
Mathematics Subject Classification ID: 15A09
Mathematics Subject Classification ID: 15A23
zbMATH DE Number: 4049795
zbMATH Keywords: intertwining matrices
zbMATH Keywords: Bézout matrices
zbMATH Keywords: Loewner matrices
zbMATH Keywords: inverses
zbMATH Keywords: Barnett factorization
reviewed by: Rabe von Randow
MaRDI profile type: Publication
full work available at URL: 0024-3795(88)90151-6
OpenAlex ID: W1980514811
cites work: Hankel and Loewner matrices
cites work: Polynomials and Hankel matrices
cites work: Intertwining and testing matrices corresponding to a polynomial
cites work: Bézoutians and intertwining matrices
cites work: Q4097423
cites work: Lyapunov, Bézout, and Hankel
cites work: Inverses of Löwner matrices
description: scientific article; zbMATH DE number 4049795