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A new class of positive semi-definite tensors

  • * Corresponding author: Jinjie Liu

    * Corresponding author: Jinjie Liu 
The first author is supported by National Natural Science Foundation of China Nos. 11501100, 11571178 and 11671082. The third author is supported in part by the Hong Kong Research Grant Council Nos. PolyU 15302114, 15300715, 15301716 and 15300717
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  • 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.

    Mathematics Subject Classification: Primary: 15A18, 15A69; Secondary: 15B99.

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