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