Eigenvariety of Nonnegative Symmetric Weakly Irreducible Tensors Associated with Spectral Radius

Yi-Zheng Fan, Yan-Hong Bao, Tao Huang

Published 2017-07-24Version 1

We proved that the projective eigenvariety of a nonnegative symmetric weakly irreducible tensor associated with the spectral radius admits a $\mathbb{Z}_m$-module structure, which is determined by the sign pattern of the tensor and can be characterized explicitly by solving the Smith norm form of the incidence matrix of the tensor. We introduced two invariants: the stability index and stability dimension based on the projective eigenvariety, which are closely related to the structure of tensors or uniform hypergraphs.