Block-matrix generalizations of Schur's basic theorems on Hadamard products
type: Item
instance of: scholarly article
title: Block-matrix generalizations of Schur's basic theorems on Hadamard products
zbMATH Open document ID: 0770.15007
DOI: 10.1016/0024-3795(92)90033-7
author: Roger A. Horn
author: Roy Mathias
published in: Linear Algebra and its Applications
publication date: 1992-09-27T00:00:00Z
review text: \textit{I. Schur} [J. Reine Angew. Math. 140, 1-28 (1911; JFM 42.0367.01)] derived a series of inequalities for the eigenvalues and the singular values of the Hadamard (entrywise) product of two matrices. Motivated by some later applications of these estimations to the theory of monotone and convex matrix functions, the authors present generalizations of a variety of Schur's inequalities for Hadamard products in which both factors are conformally partitioned block matrices, and the entries of one factor are constant within one block. Since such products turn out to be special cases of a block Kronecker product, the results are given in terms of this.
Mathematics Subject Classification ID: 15A42
Mathematics Subject Classification ID: 15A69
zbMATH DE Number: 64495
zbMATH Keywords: eigenvalues
zbMATH Keywords: singular values
zbMATH Keywords: Schur's inequalities
zbMATH Keywords: Hadamard products
zbMATH Keywords: block matrices
MaRDI profile type: Publication
full work available at URL: 0024-3795(92)90033-7
OpenAlex ID: W2091307251
cites work: Matrices Whose Powers are M-Matrices or Z-Matrices
cites work: Matrix Analysis
cites work: Q4040931
cites work: The equivalence of two partial orders on a convex cone of positive semidefinite matrices
cites work: Allowable spectral perturbations for ZME-matrices
description: scientific article; zbMATH DE number 64495