DZ-type inclusion sets of tensors with application

In this paper, we extend the Dashnic-Zusmanovic inclusion sets of matrices to the tensor case, which is proved to be always tighter than the Brauer-type inclusion sets of tensors introduced by Bu et al. (Linear Algebra Appl 512:234-248, 2017). As applications, we presented that, a DZ-type Z-tensor with nonnegative diagonal entries a strong M-tensor, and an even order DZ-type symmetric tensor with positive diagonal entries is positive definite.

Automated summary

In this paper, the Dashnic-Zusmanovic inclusion sets of matrices are extended to the tensor case, always shown to be tighter than the Brauer-type inclusion sets of tensors introduced by Bu et al. Various applications are presented, such as the properties of a DZ-type Z-tensor with nonnegative diagonal entries and a DZ-type symmetric tensor with positive diagonal entries.