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In this paper we study the joint/generalized spectral radius of a finite setof matrices in terms of its rank-one approximation by singular valuedecomposition. In the first part of the paper, we show that any finite set ofmatrices with at most one element's rank being greater than one satisfies thefiniteness property under the framework of (invariant) extremal norm. Formulafor the computation of joint/generalized spectral radius for this class ofmatrix family is derived. Based on that, in the second part, we further studythe joint/generalized spectral radius of finite sets of general matricesthrough constructing rank-one approximations in terms of singular valuedecomposition, and some new characterizations of joint/generalized spectralradius are obtained. Several benchmark examples from applications as well ascorresponding numerical computations are provided to illustrate the approach.

Rank-one Characterization of Joint Spectral Radius of Finite Matrix Family