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}
}