Two new singular value inclusion sets for rectangular tensors

ABSTRACT

Let $\mathcal{A}$ be a real $(p,q)$th order $m\times n$ dimensional rectangular tensor. A new singular value inclusion set for rectangular tensors with m=n is given and proved to be tighter than those in [Zhao JX, Li CQ. Singular value inclusion sets for rectangular tensors. Linear Multilinear A. 2018;66(7):1333–1350] and [Sang CL. An S-type singular value inclusion set for rectangular tensors. J Inequal Appl. 2017;2017:141]. Soon afterwards, this new singular value inclusion set is generalized to the general case, that is, m and n are not necessarily equal. As an application of the two sets, two upper bounds and lower bounds for the largest singular value of nonnegative rectangular tensors are obtained.

KEYWORDS:

• Rectangular tensors
• nonnegative tensors
• singular value
• inclusion sets

AMS SUBJECT CLASSIFICATIONS:

• 15A18
• 15A69

Acknowledgments

The author is grateful to the referees for their useful and constructive suggestions.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work is supported by National Natural Science Foundation of China [grant number 11501141] and Science and Technology Top-notch Talents Support Project of Education Department of Guizhou Province [grant number QJHKYZ[2016]066].