Multiplicity of singular values for tensors
type: Item
instance of: scholarly article
title: Multiplicity of singular values for tensors
zbMATH Open document ID: 1204.15020
author: Tan Zhang
author: Kung Ching Chang
published in: Communications in Mathematical Sciences
publication date: 2010-01-13T00:00:00Z
review text: There are many concepts and results of matrix theory that can be generalized to tensors. Among these, the authors are interested in the concepts of eigenvalue/eigenvector and singular values for tensors. However, the methods of matrix theory cannot be applied directly to the study of the eigenvalue and the singular value problems for tensors due to the nonlinear nature of the problem. In this paper the authors use critical point theory from nonlinear analysis and tools from algebraic topology to study the existence and multiplicity problem of singular values for higher order tensors.
Mathematics Subject Classification ID: 15A18
Mathematics Subject Classification ID: 15A69
Mathematics Subject Classification ID: 55M30
Mathematics Subject Classification ID: 58C40
zbMATH DE Number: 5657330
zbMATH Keywords: singular value
zbMATH Keywords: eigenvalue
zbMATH Keywords: tensor
zbMATH Keywords: Ljusternik-Schnirelmann theory
zbMATH Keywords: category
zbMATH Keywords: cup-length
zbMATH Keywords: multiplicity
MaRDI profile type: Publication
DOI: 10.4310/CMS.2009.V7.N3.A5
description: scientific article; zbMATH DE number 5657330