Matrix theory is one of the most fundamental tools of mathematics and science, and a
number of classical books on matrix analysis have been written to explore this theory. As a …

In this paper, using variational analysis and optimization techniques, we examine some
fundamental analytic properties of Z‐eigenvalues of a real symmetric tensor with even order …

This is a survey paper on the recent development of the spectral theory of nonnegative
tensors and its applications. After a brief review of the basic definitions on tensors, the H …

In this paper, we investigate the Laplacian, ie, the normalized Laplacian tensor of a k-
uniform hypergraph. We show that the real parts of all the eigenvalues of the Laplacian are …

Finding the maximum eigenvalue of a symmetric tensor is an important topic in tensor
computation and numerical multilinear algebra. In this paper, we introduce a new class of …

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 …

Finding the minimal H-eigenvalue of tensors is an important topic in tensor computation and
numerical multilinear algebra. This paper is devoted to a sum-of-squares (SOS) algorithm for …

Yuan's theorem of the alternative is an important theoretical tool in optimization, which
provides a checkable certificate for the infeasibility of a strict inequality system involving two …

Full article: New practical criteria for ℋ-tensors and its application Skip to Main Content Taylor
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In particle physics, the vacuum stability of scalar potentials is to check positive definiteness
(or copositivity) of its coupling tensors, and such a coupling tensor is a 4th order and …