On the Z-Eigenvalue Bounds for a Tensor

Abstract

In this paper, we first propose a $Z_p$-eigenvalue of a tensor, which includes the $Z_1$- and $Z_2$-eigenvalue as its special case, and then present a $Z_p$-eigenvalue bound. In particular, we give a $Z$-spectral radius bound for an irreducible nonnegative tensor via the spectral radius of a nonnegative matrix. The proposed bounds improve some existing ones. Some numerical examples are given to show the validity of the proposed bounds.