Asymptotic properties of powers of nonnegative matrices, with applications
type: Item
instance of: scholarly article
title: Asymptotic properties of powers of nonnegative matrices, with applications
zbMATH Open document ID: 0668.15012
DOI: 10.1016/0024-3795(89)90480-1
author: Bo Henry Lindqvist
published in: Linear Algebra and its Applications
publication date: 1989-01-01T00:00:00Z
review text: The main result of this paper gives first order approximations to \(f_ n(A)\) as \(n\to \infty\), for certain sequences \(f_ n\) of analytic functions, where A is a finite square reducible matrix in Frobenius form. In particular it holds when \(f_ n(A)=A^ n\), and hence can be used to study local behaviour of entries as well as blocks of \(A^ n\). An application to the behaviour of the vector \(pA^ n\) (``multiplicative processes'') generalizes a theorem of \textit{P. Mandl} [Casopis Pĕst. Mat. 84, 140-149 (1959; Zbl 0087.136)] who considered only non-degenerate and aperiodic diagonal blocks. The approach is via spectral properties of finite dimensional linear operators.
Mathematics Subject Classification ID: 15B48
Mathematics Subject Classification ID: 60J10
zbMATH DE Number: 4093662
zbMATH Keywords: local period
zbMATH Keywords: absorbing Markov chain
zbMATH Keywords: reducible matrix
zbMATH Keywords: Frobenius form
zbMATH Keywords: multiplicative processes
reviewed by: Eugene Seneta
MaRDI profile type: Publication
full work available at URL: 0024-3795(89)90480-1
OpenAlex ID: W2095564885
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description: scientific article; zbMATH DE number 4093662