Mathematical Sciences: Faculty Publications
An Estimation of the Spectral Radius of a Product of Block Matrices
Document Type
Article
Publication Date
3-1-2004
Publication Title
Linear Algebra and Its Applications
DOI
10.1016/S0024-3795(03)00545-7
ISSN
0024-3795
Abstract
Let C(r)=[Cij], r=1,2,…,R, be block m×m matrices where Cij(r) are nonnegative Ni×Nj matrices for i,j=1,2,…,m. Let ∥·∥ be a consistent matrix norm. Denote for each r by B(r)=[∥Cij(r)∥] an m×m matrix. The relation of the spectral radii ρ(∏r=1RC(r)) and ρ(∏r=1RB(r)) is studied in this paper. It is shown with two proofs that ρ∏r=1RC(r)⩽ρ∏r=1RB(r). Asshown in one of the proofs, ρ(∏r=1RB(r)) can be reduced so that it gives a better estimation of ρ(∏r=1RC(r)).
Recommended Citation
Chen, Mei-Qin, Xiezhang Li.
2004.
"An Estimation of the Spectral Radius of a Product of Block Matrices."
Linear Algebra and Its Applications, 379: 267-275.
doi: 10.1016/S0024-3795(03)00545-7
https://digitalcommons.georgiasouthern.edu/math-sci-facpubs/576
Copyright
This work is archived and distributed under the repository's Standard Copyright and Reuse License (opens in new tab). End users may copy, store, and distribute this work without restriction. For all other uses, permission must be obtained from the copyright owners or their authorized agents.
