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 …

Tensors, as geometric objects that describe linear or multi-linear relations between
geometric vectors, scalars, and other tensors, have provided a concise mathematical …

Moment and polynomial optimization has received high attention in recent decades. It has
beautiful theory and efficient methods, as well as broad applications for various …

Eigenvector centrality is a standard network analysis tool for determining the importance of
(or ranking of) entities in a connected system that is represented by a graph. However, many …

Several tensor eigenpair definitions have been put forth in the past decade, but these can all
be unified under generalized tensor eigenpair framework, introduced by Chang, Pearson …

We introduce the concept of mode-k generalized eigenvalues and eigenvectors of a tensor
and prove some properties of such eigenpairs. In particular, we derive an upper bound for …

This paper is devoted to generalized tensor eigenvalue problems. We focus on the
properties and perturbations of the spectra of regular tensor pairs. Employing different …

We consider the problem of decomposing a real-valued symmetric tensor as the sum of
outer products of real-valued vectors. Algebraic methods exist for computing complex …

This paper proposes a semianalytical measure of nonlinearity (MoN) based on tensor
eigenpairs. Approximating nonlinear dynamics via local linearization is a common practice …

This paper presents the neural dynamical network to compute a best rank-one
approximation of a real-valued tensor. We implement the neural network model by the …