Some Properties of the Strong Primitivity of Nonnegative Tensors

Abstract

We show that an order $m$ dimension 2 tensor is primitive if and only if its majorization matrix is primitive, and then we obtain the characterization of order $m$ dimension 2 strongly primitive tensors and the bound of the strongly primitive degree. Furthermore, we study the properties of strongly primitive tensors with $n\ge \mathrm{3}$ and propose some problems for further research.