A limit theorem for monotone matrix functions
type: Item
instance of: scholarly article
title: A limit theorem for monotone matrix functions
zbMATH Open document ID: 0822.15001
DOI: 10.1016/0024-3795(93)90122-5
author: Werner Kratz
published in: Linear Algebra and its Applications
publication date: 1995-10-15T00:00:00Z
review text: The author considers the limit problem for symmetric matrix functions and proves that if \(Q(t)= U(t) X^{-1}(t)\) is a symmetric \(m\times m\) matrix function which decreases on some interval \((0, \varepsilon)\) and \(U(t)\to U\), \(X(t)\to X\) as \(t\to 0^ +\) with \(\text{rank}(U^ T, X^ T)= m\), then \(\lim_{t\to 0^ +} X^ T Q(t) X= U^ T X\) and \(\lim_{t\to 0^ +} c^ T Q(t) c= \infty\) for all \(c \overline\in \text{ Im}(X)\).
reviewed by: Shaokuan Li
Mathematics Subject Classification ID: 15A23
Mathematics Subject Classification ID: 15A60
Mathematics Subject Classification ID: 15A54
zbMATH DE Number: 540065
zbMATH Keywords: limit theorem
zbMATH Keywords: monotone matrix functions
zbMATH Keywords: symmetric matrix functions
MaRDI profile type: Publication
full work available at URL: 0024-3795(93)90122-5
OpenAlex ID: W2063542420
cites work: A general oscillation theorem for self-adjoint differential systems with applications to Sturm-Liouville eigenvalue problems and quadratic functionals
cites work: Q3999241
cites work: A Substitute of L'Hospital's Rule for Matrices
cites work: A TREATMENT OF STURM-LIOUVILLE EIGENVALUE PROBLEMS VIA PICONE'S IDENTITY
cites work: Q5674306
description: scientific article; zbMATH DE number 540065