Minimal Gersgorin tensor eigenvalue inclusion set and its numerical approximation

Abstract

For a complex tensor A, Minimal Gersgorin tensor eigenvalue inclusion set of A is presented, and its sufficient and necessary condition is given. Furthermore, we study its boundary by the spectrums of the equimodular set and the extended equimodular set for A. Lastly, for an irreducible tensor, a numerical approximation to Minimal Gersgorin tensor eigenvalue inclusion set is given.