On the uniqueness of the positive Z-eigenvector for nonnegative tensors

Abstract The uniqueness of positive Z-eigenvector of nonnegative tensors has many important applications in both theory and practical application. In this paper, we give a sufficient condition that a nonnegative tensor has unique positive Z-eigenvector by using its entries. For the third order transition probabilities tensor, we show that its positive Z-eigenvector corresponding to eigenvalue 1 is unique.