CONVERGENCE OF INHOMOGENOUS PRODUCTS OF MATRICES AND COEFFICIENTS OF ERGODICITY

Authors
HARTFIEL DJ ROTHBLUM UG
Citation
Dj. Hartfiel et Ug. Rothblum, CONVERGENCE OF INHOMOGENOUS PRODUCTS OF MATRICES AND COEFFICIENTS OF ERGODICITY, Linear algebra and its applications, 277(1-3), 1998, pp. 1-9
Citations number
9
Categorie Soggetti
Mathematics,Mathematics
Journal title
Linear algebra and its applications → ACNP
ISSN journal
00243795
Volume
277
Issue
1-3
Year of publication
1998
Pages
1 - 9
Database
ISI
SICI code
0024-3795(1998)277:1-3<1:COIPOM>2.0.ZU;2-X
Abstract
Given a square matrix A and a norm II ii, the coefficient of ergodicit y of A with respect to parallel to parallel to is defined as max {para llel to x(T)All; x is an element of R-n, parallel to x parallel to = 1 , x(T)F = 0} with F as a matrix satisfying AF = 0. We demonstrate that for a bounded set of such matrices with all coefficients of ergodicit y of the matrices in the set below 1, all sequences constructed throug h inhomogenous products of matrices from the set converge geometricall y. (C) 1998 Elsevier Science Inc. All rights reserved.