-inclusion sets for eigenvalues of a tensor. Issue 5 (4th May 2018)

• Record Type: Journal Article
• Authors: Lei, Xiaoqiang
• Is Part Of: Linear & multilinear algebra. Volume 66:Issue 5(2018)
• Page Start: 942
• Page End: 960
• Publication Date: 2018-05-04
• Subjects: Tensor -- eigenvalue -- inclusion -- -region -- -tensor; 15A69 -- 15A18 -- 65F15 -- 65H17 -- 15A15 -- 65F40; Algebras, Linear -- Periodicals; Multilinear algebra -- Periodicals; 512.505
• DOI: 10.1080/03081087.2017.1331996
• Languages: English
• ISSNs: 0308-1087

Abstract

Abstract: In this paper, we mainly focus on new inclusion sets for eigenvalues of a tensor. First, we propose new inclusion sets for eigenvalues of a tensor, which are sharper than some existing inclusion sets, and obtain the law of distribution of the number of eigenvalues for a tensor. Second, two new classes of tensors are introduced. Third, some bounds on the spectral radii for nonnegative tensors are given. Fourth, some checkable sufficient conditions for the positive definiteness (positive semidefiniteness) of some classes of even-order real symmetric tensors are obtained.