An eigenvalue localization set for tensors with applications to determine the positive (semi-)definiteness of tensors. Issue 4 (2nd April 2016)

• Record Type: Journal Article
• Authors: Li, Chaoqian; Li, Yaotang
• Is Part Of: Linear & multilinear algebra. Volume 64:Issue 4(2016)
• Page Start: 587
• Page End: 601
• Publication Date: 2016-04-02
• Subjects: tensor eigenvalue -- localization set -- positive definite -- positive semi-definite; 15A69 -- 15A18; Algebras, Linear -- Periodicals; Multilinear algebra -- Periodicals; 512.505
• DOI: 10.1080/03081087.2015.1049582
• Languages: English
• ISSNs: 0308-1087

Abstract

Abstract : A new eigenvalue localization set for tensors is given, and proved to be tighter than those in [Qi L. Eigenvalues of a real supersymmetric tensor. J. Symbolic Comput. 2005;40:1302–1324] and [Li CQ, Li YT, Kong X. New eigenvalue inclusion sets for tensors. Numer. Linear Algebra Appl. 2014;21:39–50]. Based on this set, we give two checkable sufficient conditions of the positive definiteness of tensors, and two checkable sufficient conditions of the positive semi-definiteness of tensors.