Bounds for joint spectral radii of a set of nonnegative matrices
For a finite set \(\Sigma\) of nonnegative matrices of order \(n\) the upper and lower joint spectral radius is defined. Bounds for these magnitudes are given in terms of the following matrix \(S=(s_{ij})\), where \(s_{ij} = \max\{\sum_ka_{ik}:A \in \Sigma, a_{ij} >0\}\) and in terms of the similarly defined matrix \(S^-\). It is shown that the upper joint spectral radius is bounded by the max spectral radius of \(S\) and that a similar result holds for the lower joint spectral radius. This generalizes results for the case of one matrix. In the proof methods of max algebra are used.
scientific article; zbMATH DE number 5791014