Infinite products of uniformly paracontracting matrices

Abstract

We define uniform paracontraction for an arbitrary set of matrices and show that an infinite product of matrices drawn from a uniformly paracontracting set is convergent. Moreover, if the uniformly paracontracting set is finite and the matrices are drawn in a regulated way, the infinite product is exponentially convergent.

Keywords:

• infinite matrix product
• uniformly paracontracting

AMS Subject Classifications:

• 65F10
• 47H09
• 15A99

Acknowledgements

The authors would like to thank the referee for the helpful comments and suggestions that helped to improve the paper.

Notes

No potential conflict of interest was reported by the authors.