Using a result linking convexity and irreducibility of matrix sets it is shown that the generalized spectral radius of a compact set of matrices is a strictly increasing function of the set in a very natural sense. As an application some consequences of t

We give sufficient conditions for existence of a perfect matching in a graph in terms of the eigenvalues of the Laplacian matrix. We also show that a distance-regular graph of degree k is k-edge-connected.