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

Abstract

We study the finite-step realizability of the joint/generalized spectral radius of a pair of real $d\times d$ matrices, one of which has rank 1. Then we prove that there always exists a finite-length word for which there holds the spectral finiteness property for the set of matrices under consideration. This implies that stability is algorithmically decidable in our case.

14 pages, 61 bibliography references

Cited by in corpus (4)

• Rank-one Characterization of Joint Spectral Radius of Finite Matrix Family
• Finiteness Property of a Bounded Set of Matrices with Uniformly Sub-Peripheral Spectrum
• Hourglass alternative and the finiteness conjecture for the spectral characteristics of sets of non-negative matrices
• A criterion of simultaneously symmetrization and spectral finiteness for a finite set of real 2-by-2 matrices