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| Main Author: | |
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| Format: | Preprint |
| Published: |
2017
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/1712.06356 |
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Table of Contents:
- We consider the problem of convergence to zero of matrix products $A_{n}B_{n}\cdots A_{1}B_{1}$ with factors from two sets of matrices, $A_{i}\in\mathscr{A}$ and $B_{i}\in\mathscr{B}$, due to a suitable choice of matrices $\{B_{i}\}$. It is assumed that for any sequence of matrices $\{A_{i}\}$ there is a sequence of matrices $\{B_{i}\}$ such that the corresponding matrix product $A_{n}B_{n}\cdots A_{1}B_{1}$ converges to zero. We show that in this case the convergence of the matrix products under consideration is uniformly exponential, that is, $\|A_{n}B_{n}\cdots A_{1}B_{1}\|\le Cλ^{n}$, where the constants $C>0$ and $λ\in(0,1)$ do not depend on the sequence $\{A_{i}\}$ and the corresponding sequence $\{B_{i}\}$.