The finite-step realizability of the joint spectral radius of a pair of d× 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× 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.
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