Journal
JAPAN JOURNAL OF INDUSTRIAL AND APPLIED MATHEMATICS
Volume 39, Issue 1, Pages 165-176Publisher
SPRINGER JAPAN KK
DOI: 10.1007/s13160-021-00482-y
Keywords
Dashnic-Zusmanovic type inclusion sets; Brauer-type inclusion sets; DZ-type tensor; Positive definite
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Funding
- NSF of China [71461027]
- Guizhou Province Natural Science Foundation in China [Qian Jiao He KY [2020]094]
- Science and Technology Foundation of Guizhou Province [Qian Ke He Ji Chu ZK[2021]Yi Ban 014]
- Innovative talent team in Guizhou Province [Qian Ke He Pingtai Rencai[2016]5619]
- New academic talents and innovative exploration fostering project [Qian Ke He Pingtai Rencai[2017]5727-21]
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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.
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.
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