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Research articles

ScienceAsia 47 (2021): 257-263 |doi: 10.2306/scienceasia1513-1874.2021.035

Rectangular M-tensors and strong rectangular M-tensors

Jun He*, Yanmin Liu, Guangjun Xu

ABSTRACT:     In this paper, two new classes of rectangular tensors called rectangular M-tensors and strong rectangular M-tensors are introduced. It is shown that an even-order partially symmetric rectangular M-tensor is positive semidefinite and an even-order partially symmetric strong rectangular M-tensor is positive definite. As a generalization of rectangular M-tensors, we introduce the rectangular H-tensors. In addition, some properties of (strong) rectangular M-tensors are established.

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a School of Mathematics, Zunyi Normal College, Zunyi, Guizhou 563006 China

* Corresponding author, E-mail: hejunfan1@163.com

Received 23 Sep 2020, Accepted 23 Feb 2021