ABSTRACT
Let be a real
th order
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.
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.