The Relation Between a Tensor and Its Associated Semi-Symmetric Form  

作　　者：Hassan Bozorgmanesh Masoud Hajarian Anthony Theodore Chronopoulos 

机构地区：[1]Department of Applied Mathematics,Faculty of Mathematical Sciences,Shahid Beheshti University,Tehran,Iran [2]Department of Computer Science,University of Texas,San Antonio,Texas 78249,USA [3](Visiting Faculty)Department of Computer Engineering&Informatics,University of Patras,Rio 26500,Greece

出　　处：《Numerical Mathematics(Theory,Methods and Applications)》2022年第2期530-564,共35页高等学校计算数学学报（英文版）

摘　　要：It is known that every tensor has an associated semi-symmetric tensor.The purpose of this paper is to investigate the shared properties of a tensor and its semi-symmetric form.In particular,a corresponding semi-symmetric tensor has smaller Frobenius norm under some conditions and can be used to get smaller bounds for eigenvalues and solutions of dynamical systems and tensor complementarity problems.In addition,every tensor has the same eigenvalues as its corresponding semi-symmetric form,also a corresponding semi-symmetric tensor inherits properties like being circulant,Toeplitz,Z-tensor,M-tensor,H-tensor and some others.Also,there are a two-way connection for properties like being positive definite,P-tensor,semi-positive,primitive and several others.

关 键 词：Tensor eigenvalue semi-symmetric tensor eigenvalue bound logarithmic norm tensor complementarity problem 

分 类 号：O15[理学—数学]