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On determinants and eigenvalue theory of tensors

We investigate properties of the determinants of tensors, and their applications in the eigenvalue theory of tensors. We show that the determinant inherits many properties of the determinant of a… Expand

The Laplacian of a uniform hypergraph

Abstract In this paper, we investigate the Laplacian, i.e., the normalized Laplacian tensor of a $$k$$-uniform hypergraph. We show that the real parts of all the eigenvalues of the Laplacian are in… Expand

The eigenvectors associated with the zero eigenvalues of the Laplacian and signless Laplacian tensors of a uniform hypergraph

In this paper, we show that the eigenvectors associated with the zero eigenvalues of the Laplacian and signless Laplacian tensors of a k-uniform hypergraph are closely related to some configured… Expand

Finding the extreme Z-eigenvalues of tensors via a sequential semidefinite programming method

SUMMARY
In this paper, we first introduce the tensor conic linear programming (TCLP), which is a generalization of the space TCLP. Then an approximation method, by using a sequence of semidefinite… Expand

Error Bounds for the Solution Sets of Quadratic Complementarity Problems

In this article, two types of fractional local error bounds for quadratic complementarity problems are established, one is based on the natural residual function and the other on the standard… Expand

A generalized Newton method for absolute value equations associated with second order cones

In this paper, we introduce the absolute value equations associated with second order cones (SOCAVE in short), which is a generalization of the absolute value equations discussed recently in the… Expand

Finding the Maximum Eigenvalue of Essentially Nonnegative Symmetric Tensors via Sum of Squares Programming

Finding the maximum eigenvalue of a tensor is an important topic in tensor computation and multilinear algebra. Recently, for a tensor with nonnegative entries (which we refer it as a nonnegative… Expand

An iterative algorithm for third-order tensor multi-rank minimization

Recent work by Kilmer et al. (A third-order generalization of the matrix SVD as a product of third-order tensors, Department of Computer Science, Tufts University, Medford, MA, 2008; Linear Algebra… Expand

A Tensor Analogy of Yuan’s Theorem of the Alternative and Polynomial Optimization with Sign structure

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… Expand

Theorems of the Alternative for Inequality Systems of Real Polynomials

In this paper, we establish theorems of the alternative for inequality systems of real polynomials. For the real quadratic inequality system, we present two new results on the matrix decomposition,… Expand