Singular value inclusion sets of rectangular tensors

In this paper, two singular value inclusion sets for rectangular tensors via a digraph and a lifting square tensor are given, respectively. Furthermore, it is shown that these two singular value inclusion sets are both tighter than the known result given by Zhao and Li in Theorem 2.1 of [25], and si...

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Bibliographic Details
Published inLinear algebra and its applications Vol. 576; pp. 181 - 199
Main Authors Yao, Hongmei, Zhang, Can, Liu, Lei, Zhou, Jiang, Bu, Changjiang
Format Journal Article
LanguageEnglish
Published Amsterdam Elsevier Inc 01.09.2019
American Elsevier Company, Inc
Subjects
Digraph
Graph theory
Hoisting
Lifting square tensor
Linear algebra
Mathematical analysis
Rectangular tensor
Singular value inclusion set
Tensors
Singular value inclusion set
15A69
Digraph
Rectangular tensor
Lifting square tensor
15A18
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Summary:In this paper, two singular value inclusion sets for rectangular tensors via a digraph and a lifting square tensor are given, respectively. Furthermore, it is shown that these two singular value inclusion sets are both tighter than the known result given by Zhao and Li in Theorem 2.1 of [25], and singular value inclusion sets via a digraph in special case are tighter than the inclusion sets via a lifting square tensor, numerical examples are still given to show the relation among the inclusion sets via a digraph, the inclusion sets via a lifting square tensor and the known result given by Zhao and Li [25]. Finally, by using the lifting square tensors, the result of tensors provided by Bu et al. [24] is extended to rectangular tensors.
ISSN:0024-3795
1873-1856
DOI:10.1016/j.laa.2018.05.011