Finiteness Property of a Bounded Set of Matrices with Uniformly Sub-Peripheral Spectrum

Abstract

In the paper, a simple condition guaranteing the finiteness property for a bounded set of matrices is presented. Given a bounded set S of real or complex matrices, it is shown that existence of a sequence of matrix products such that the spectrum of each matrix in this sequence is uniformly sub-peripheral and tends to the joint spectral radius of S, guarantees the spectral finiteness property for S.

8 pages, 29 bibliography references. Minor changes in v3

References in corpus (1)

• The finite-step realizability of the joint spectral radius of a pair of $d\times d$ matrices one of which being rank-one

Cited by in corpus (6)

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• Finer filtration for matrix-valued cocycle based on Oseledec's multiplicative ergodic theorem
• Stability Criteria via Common Non-strict Lyapunov Matrix for Discrete-time Linear Switched Systems
• Some criteria for spectral finiteness of a finite subset of the real matrix space ${\mathbb{R}}^{d\times d}$
• A criterion of simultaneously symmetrization and spectral finiteness for a finite set of real 2-by-2 matrices