A NEW CLASS OF POSITIVE SEMI-DEFINITE TENSORS

JOURNAL OF INDUSTRIAL AND MANAGEMENT OPTIMIZATION（2020）

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摘要

In this paper, a new class of positive semi-definite tensors, the MO tensor, is introduced. It is inspired by the structure of Moler matrix, a class of test matrices. Then we focus on two special cases in the MO-tensors: Sup-MO tensor and essential MO tensor. They are proved to be positive definite tensors. Especially, the smallest H-eigenvalue of a Sup-MO tensor is positive and tends to zero as the dimension tends to infinity, and an essential MO tensor is also a completely positive tensor.

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关键词

Positive (semi-)definite tensor,completely positive tensor,H-eigenvalue,MO-tensor,MO-like tensor,Sup-MO value

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