On the estimates of the Z-eigenpair for an irreducible nonnegative tensor

In this paper, we are concerned with the Z-eigenpair of a tensor, in particular, an irreducible nonnegative tensor. Some new lower and upper bounds for the eigenvector and Z-spectral radius of an irreducible (weakly symmetric) nonnegative tensors are provided. Our new bounds, which mostly generalize the ones presented in Li et al. (2015) [13], are closely related to the order of a tensor and proved to be tighter than those there. A new bound for Z1-eigenvalue of general tensors is specifically presented. Some examples are given to show the sharpness of our new bounds in contrast with the known ones, including the comparison results with the very recent research by other authors in the Appendix.