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 …

This paper devotes to the generalized eigenvalues for even order tensors. We extend
classical spectral theory for matrix pairs to the multilinear case, including the generalized …

In this paper, we intend to solve the multi-linear system by preconditioned iterative method
based on tensor splitting. We propose a new preconditioner I+ S ma x. In order to compare …

Recently, the inverse of an even-order square tensor has been put forward in [Brazell M, Li
N, Navasca C, Tamon C. Solving multilinear systems via tensor inversion. SIAM J Matrix …

Recently, the tensor nuclear norm (TNN), which is the convex surrogate for tensor multi rank,
has been successfully applied to the low-rank tensor completion (LRTC) problem. However …

In biological and engineering systems, structure, function and dynamics are highly coupled.
Such interactions can be naturally and compactly captured via tensor based state space …

This paper proposes an algorithm based on the Shultz iterative method and divided
differences to find the roots of nonlinear equations. Using the new method, we present a …

The main purpose of this paper is devoted to solving the multi-linear systems by the
preconditioned methods based on the tensor splittings. We consider a new preconditioner I+ …

In this paper, we provide a system theoretic treatment of a new class of multilinear time-
invariant (MLTI) systems in which the states, inputs, and outputs are tensors, and the system …

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 …