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A New Class of Positive Semi-definite Tensors

Spectral Theory 2018-09-26 v3

Abstract

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.

Keywords

Cite

@article{arxiv.1611.06035,
  title  = {A New Class of Positive Semi-definite Tensors},
  author = {Yi Xu and Jinjie Liu and Liqun Qi},
  journal= {arXiv preprint arXiv:1611.06035},
  year   = {2018}
}