Basic Properties of the Projective Product with Application to Products of Column-Allowable Nonnegative Matrices 2000 11 citations ? 0 self

Abstract:  We use basic properties of the projective product, to obtain exponential bounds for the Lipschitz constant associated with the projective product of column--allowable nonnegative matrices. We obtain similar bounds for the associated linear tangent maps. Keywords : projective product, Birkhoff contraction coefficient, cocycle, exponential forgetting, product of matrices. This work was partially supported by the Commission of the European Communities, under the SCIENCE project System Identification, project number SC1*--CT92--0779, and under the HCM project Statistical Inference for Stochastic Processes, project number CHRX--CT92--0078, by the French--Hungarian cooperation program BALATON, project number 96--036, and by the Army Research Office, under grant DAAH04--95--1--0164. Contents 1 Introduction 1 2 Contraction coefficients and basic properties of the projective product 1 3 Application to products of matrices 4 4 First--order properties of the projective product 7 5 Applicati...