Abstract

ABSTRACTLet 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.

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