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 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.