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

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

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.

Author Details

Masoud Hajarian

Hassan Bozorgmanesh

Anthony Theodore Chronopoulos

Masoud Hajarian

Anthony Theodore Chronopoulos

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