Year: 2022
Author: Masoud Hajarian, Hassan Bozorgmanesh, Anthony Theodore Chronopoulos, Masoud Hajarian, Anthony Theodore Chronopoulos
Numerical Mathematics: Theory, Methods and Applications, Vol. 15 (2022), Iss. 2 : pp. 530–564
Abstract
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.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/nmtma.OA-2021-0164
Numerical Mathematics: Theory, Methods and Applications, Vol. 15 (2022), Iss. 2 : pp. 530–564
Published online: 2022-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 35
Keywords: Tensor eigenvalue semi-symmetric tensor eigenvalue bound logarithmic norm tensor complementarity problem.