A new Brauer-type Z -eigenvalue inclusion set for even-order tensors

A new Brauer-type Z -eigenvalue inclusion set for an even-order real tensor is presented. It is proved that it is tighter than the existing inclusion sets. As an application, a sufficient condition for the positive definiteness of an even-order real symmetric tensor (also a homogeneous polynomial form) and asymptotically stability of time-invariant polynomial systems is given.