Please use this identifier to cite or link to this item: http://hdl.handle.net/10397/21405
Title: Symmetric nonnegative tensors and copositive tensors
Authors: Qi, L 
Keywords: Copositive tensor
H-eigenvalue
Nonnegative tensor
Issue Date: 2013
Source: Linear algebra and its applications, 2013, v. 439, no. 1, p. 228-238 How to cite?
Journal: Linear Algebra and Its Applications 
Abstract: We first prove two new spectral properties for symmetric nonnegative tensors. We prove a maximum property for the largest H-eigenvalue of a symmetric nonnegative tensor, and establish some bounds for this eigenvalue via row sums of that tensor. We show that if an eigenvalue of a symmetric nonnegative tensor has a positive H-eigenvector, then this eigenvalue is the largest H-eigenvalue of that tensor. We also give a necessary and sufficient condition for this. We then introduce copositive tensors. This concept extends the concept of copositive matrices. Symmetric nonnegative tensors and positive semi-definite tensors are examples of copositive tensors. The diagonal elements of a copositive tensor must be nonnegative. We show that if each sum of a diagonal element and all the negative off-diagonal elements in the same row of a real symmetric tensor is nonnegative, then that tensor is a copositive tensor. Some further properties of copositive tensors are discussed.
URI: http://hdl.handle.net/10397/21405
ISSN: 0024-3795
DOI: 10.1016/j.laa.2013.03.015
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