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

2011/06/05 by Xiongping Dai, Dai, Xiongping · 1 citation
Computer Science · Engineering · Mathematics · #65F15 #93D20 #Advanced Topics in Algebra #Dynamical Systems (math.DS) #FOS: Electrical engineering #FOS: Mathematics #Matrix Theory and Algorithms #Optimization and Control (math.OC) #Primary 15B52 #Secondary 15A60 #Systems and Control (eess.SY) #electronic engineering #graph theory and CDMA systems #information engineering

paper · pdf · doi:10.48550/arxiv.1106.0870

openalex publication_date 2011/06/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study the finite-step realizability of the joint/generalized spectral radius of a pair of real d× 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.

Cited by

• A criterion of simultaneously symmetrization and spectral finiteness for a finite set of real 2-by-2 matrices

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