A convexity lemma on the interlacing inequalities for invariant factors
type: Item
instance of: scholarly article
title: A convexity lemma on the interlacing inequalities for invariant factors
zbMATH Open document ID: 0659.15019
DOI: 10.1016/0024-3795(88)90201-7
author: E. Marques de Sá
published in: Linear Algebra and its Applications
publication date: 1988-01-01T00:00:00Z
review text: A simple proof is given for a lemma on divisibility of polynomials that was stated in an earlier paper of the author [ibid. 24, 33-50 (1979; Zbl 0395.15009)]. Two generalizations of the lemma are also stated. Reviewer's note: The presentation of the results is not complete, as the function \(\Delta\) (s) of Section 2 is - notwithstanding the author's assertion - not convex. The following data may serve as a simple counterexample: \(a_ i=b_ i=0\) for \(i\leq 0\), \(a_ 1=a_ 2=a_ 3=1\), \(a_ 4=2\), \(a_ i=i-1\) for \(i\geq 5\), \(b_ i=i\) for \(i\geq 1\); \(n=5.\) [Editorial remark: According to the reviewer's comment a correction has been submitted for this paper.]
Mathematics Subject Classification ID: 15A45
Mathematics Subject Classification ID: 15A15
Mathematics Subject Classification ID: 12E05
zbMATH DE Number: 4077449
zbMATH Keywords: invariant factors
zbMATH Keywords: convexity
zbMATH Keywords: interlacing inequalities
zbMATH Keywords: divisibility of polynomials
reviewed by: László Mihályffy
MaRDI profile type: Publication
full work available at URL: 0024-3795(88)90201-7
OpenAlex ID: W2115389623
Wikidata QID: Q124820850
cites work: Q5638112
cites work: Q4405392
cites work: Imbedding conditions for \(\lambda\)-matrices
cites work: Interlacing inequalities for invariant factors
description: scientific article; zbMATH DE number 4077449