Convexity of the dominant eigenvalue of an essentially nonnegative matrix

Authors: Joel E. Cohen - Proceedings of the American Mathematical Society 1981 cited by 86

The dominant eigenvalue of a real n x n matrix A with nonnegative elements off the main diagonal is a convex function of the diagonal of A. We give a short proof using Trotter's product formula and a theorem on log-convexity due to Kingman.