Some bounds for the spectral radius of nonnegative tensors

Abstract

© 2014, Springer-Verlag Berlin Heidelberg. In this paper, we extend the well-known column sum bound of the spectral radius for nonnegative matrices to the tensor case, an upper bound of the spectral radius for a nonnegative tensor is given via the largest eigenvalue of a symmetric tensor. Also we show some bounds of spectral radius of nonnegative tensors based on the sum of the entries in the other indices of tensors. We demonstrate that our new results improve existing results. The other main results of this paper is to provide a sharper Ky Fan type theorem and a comparison theorem for nonnegative tensors. Finally, we make use of our bounds to give a perturbation bound for the spectral radius of symmetric nonnegative tensors. This result is similar to the Weyl theorem for the matrix case.