TY - JOUR
A2 - Kulenovic, Mustafa R. S.
AU - Kozyakin, Victor
PY - 2018
DA - 2018/04/22
TI - On Convergence of Infinite Matrix Products with Alternating Factors from Two Sets of Matrices
SP - 9216760
VL - 2018
AB - We consider the problem of convergence to zero of matrix products AnBn⋯A1B1 with factors from two sets of matrices, Ai∈A and Bi∈B, due to a suitable choice of matrices {Bi}. It is assumed that for any sequence of matrices {Ai} there is a sequence of matrices {Bi} such that the corresponding matrix products AnBn⋯A1B1 converge to zero. We show that, in this case, the convergence of the matrix products under consideration is uniformly exponential; that is, AnBn⋯A1B1≤Cλn, where the constants C>0 and λ∈(0,1) do not depend on the sequence {Ai} and the corresponding sequence {Bi}. Other problems of this kind are discussed and open questions are formulated.
SN - 1026-0226
UR - https://doi.org/10.1155/2018/9216760
DO - 10.1155/2018/9216760
JF - Discrete Dynamics in Nature and Society
PB - Hindawi
KW -
ER -