Based on Turan's power sum theory, we extend a recent result obtained by Blondel and Nesterov [Blondel, V. D., & Nesterov, Y. (2005). Computationally efficient approximations of the joint spectral radius, SIAM Journal on Matrix Analysis and Applications, 27, 256-272], by deriving a new characterization of the generalized spectral radius in terms of Kronecker powers. (C) 2011 Elsevier Ltd. All rights reserved.