<i>Z</i>-Eigenvalue Inclusion Theorems for Tensors

Abstract

In this paper, we establish $Z$-eigenvalue inclusion theorems for general tensors, which reveal some crucial differences between $Z$-eigenvalues and $H$-eigenvalues. As an application, we obtain upper bounds for the largest $Z$-eigenvalue of a weakly symmetric nonnegative tensor, which are sharper than existing upper bounds.