The Z-eigenpairs of orthogonally diagonalizable symmetric tensors

Abstract

In this paper, we focus on a special class of symmetric tensors, which can be orthogonally diagonalizable, and investigate their Z-eigenpairs problem. We show that the eigenpairs can be uniformly expressed using several basic eigenpairs, and the number of all the eigenpairs is uniquely determined by the order and rank of the symmetric tensor. In addition, we exploit the local optimality of each eigenpair by checking the second-order necessary condition.