An estimation of the spectral radius of a product of block matrices.
type: Item
instance of: scholarly article
title: An estimation of the spectral radius of a product of block matrices.
zbMATH Open document ID: 1043.15012
DOI: 10.1016/S0024-3795(03)00545-7
author: Meiqin Chen
author: Xiezhang Li
published in: Linear Algebra and its Applications
publication date: 2004-03-14T00:00:00Z
review text: Let \(C(r)= \lfloor C_{ij}\rfloor\), \(r= 1,2,\dots, R\), be block \(m\times m\) matrices, where \(C_{ij}(r)\) are nonnegative \(N_i\times N_j\) matrices for \(i,j= 1,2,\dots, m\). For each \(r\) let \(B(r)= \lfloor\| C_{ij}(r)\|\rfloor\) be the \(m\times m\) matrix, where \(\|\cdot\|\) denotes a consistent norm. The authors, among other results, give an estimation of the spectral radius of a product of block matrices. They show that \[ \rho\Biggl(\prod^R_{r=1} C(r)\Biggr)\leq \rho\Biggl(\prod^R_{r=1} B(r)\Biggr), \] where \(\rho(A)\) denotes the spectral radius of the matrix \(A\).
reviewed by: Omar Hirzallah
Mathematics Subject Classification ID: 15A42
Mathematics Subject Classification ID: 15B48
zbMATH DE Number: 2056689
zbMATH Keywords: Nonnegative matrices
zbMATH Keywords: Spectral radius
zbMATH Keywords: Block matrices
MaRDI profile type: Publication
cites work: Stability of two-dimensional discrete systems with periodic coefficients
cites work: Matrix Analysis
cites work: Q4947421
cites work: Q3870224
description: scientific article; zbMATH DE number 2056689