Some bounds for the Z-eigenpair of nonnegative tensors

Tensor eigenvalue problem is one of important research topics in tensor theory. In this manuscript, we consider the properties of Z-eigenpair of irreducible nonnegative tensors. By estimating the ratio of the smallest and largest components of a positive Z-eigenvector for a nonnegative tensor, we present some bounds for the eigenvector and Z-spectral radius of an irreducible and weakly symmetric nonnegative tensor. The proposed bounds complement and extend some existing results. Finally, several examples are given to show that such a bound is different from one given in the literature.