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

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

2011-06-05

arxiv.org/abs/1106.0870v1

Mathematics

Optimization and Control

14 pages, 61 bibliography references

Scientific paper

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.

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