C-eigenvalue inclusion theorems for piezoelectric-type tensors
type: Item
instance of: scholarly article
title: C-eigenvalue inclusion theorems for piezoelectric-type tensors
zbMATH Open document ID: 1444.15013
published in: Applied Mathematics Letters
publication date: 2019-02-20T00:00:00Z
review text: Let \(\mathcal A=(a_{ijk})\) be an \(n\times n\times n\) real tensor. If \(a_{ijk}=a_{ikj}\) for all values of indices, then \(\mathcal A\) is called piezoelectric-type tensor. Let \(\mathcal C=(c_{ijk})\) be another \(n\times n\times n\) real tensor. If there exist a real scalar \(\lambda\) and real norm one \(n\times 1\) vectors \(x\) and \(y\) such that \(\mathcal A yy =\lambda x\), \(x\mathcal A y =\lambda y\), where \(\mathcal A yy\) and \(x\mathcal A y \) denote vectors with the entries, \(\sum_{i,k}c_{ijk}y_iy_k\) and \(\sum_{k,j}c_{kji}x_ky_j\), respectively, then \(\lambda\) is called a \(C\)-eigenvalue of \(\mathcal A\), and \(x\) and \(y\) are called associated left and right \(C\)-eigenvectors, respectively. The authors present three inclusion theorems to locate all \(C\)-eigenvalues for a given piezoelectric-type tensor.
Mathematics Subject Classification ID: 15A69
Mathematics Subject Classification ID: 15A18
zbMATH DE Number: 7026080
zbMATH Keywords: C-eigenvalue
zbMATH Keywords: C-eigenvector
zbMATH Keywords: piezoelectric-type tensors
zbMATH Keywords: localization theorem
author: Hai-Tao Che
author: Haibin Chen
author: Yiju Wang
reviewed by: Ignat Domanov
MaRDI profile type: Publication
Wikidata QID: Q114210641
full work available at URL: j.aml.2018.09.014
OpenAlex ID: W2895349093
cites work: Tensor properties of crystals.
cites work: Q3243972
cites work: Octupolar tensors for liquid crystals
cites work: Copositivity detection of tensors: theory and algorithm
cites work: A semidefinite program approach for computing the maximum eigenvalue of a class of structured tensors and its applications in hypergraphs and copositivity test
cites work: Copositive tensor detection and its applications in physics and hypergraphs
cites work: On computing minimal \(H\)-eigenvalue of sign-structured tensors
cites work: Column sufficient tensors and tensor complementarity problems
cites work: Convergence analysis of a block improvement method for polynomial optimization over unit spheres
cites work: Criteria for strong \(H\)-tensors
cites work: A fast algorithm for the spectral radii of weakly reducible nonnegative tensors
cites work: An \(H\)-tensor based iterative scheme for identifying the positive definiteness of multivariate homogeneous forms
cites work: Solution structures of tensor complementarity problem
cites work: A practical method for computing the largestM-eigenvalue of a fourth-order partially symmetric tensor
cites work: Eigenvalues of a real supersymmetric tensor
cites work: Q4479208
cites work: Q4829998
cites work: New eigenvalue inclusion sets for tensors
cites work: A new Brauer-type eigenvalue localization set for tensors
cites work: An eigenvalue localization set for tensors with applications to determine the positive (semi-)definiteness of tensors
cites work: An \(S\)-type eigenvalue localization set for tensors
cites work: Brualdi-type eigenvalue inclusion sets of tensors
cites work: \(Z\)-eigenvalue inclusion theorems for tensors
DOI: 10.1016/J.AML.2018.09.014
description: scientific article; zbMATH DE number 7026080