Maximizing the spectral radius of fixed trace diagonal perturbations of nonnegative matrices Original Research Article

Let A be an n-by-n irreducible, entrywise nonnegative matrix. For a given t> 0, we consider the problem of maximizing the Perron root of a nonnegative, diagonal, trace t perturbation of A. Because of the convexity of the Perron root as a function of diagonal entries, the maximum occurs for some tEii. Such an index i, which is called a winner, may depend on t. We show how to determine the (nonempty) set of indices i that are winners for all sufficiently small t and the possibly different (nonempty) set of indices that are winners for all sufficiently large t. We also show how to determine if there are indices that are winners for all t.