Completely Positive Biquadratic Tensors
Rings and Algebras
2025-10-14 v1
Abstract
In this paper, we systemically introduce completely positive biquadratic (CPB) tensors and copositive biquadratic tensors. We show that all weakly CPB tensors are sum of squares tensors, the CPB tensor cone and the copositive biquadratic tensor cone are dual cone to each other. We also show that the outer product of two completely positive matrices is a CPB tensor, and the outer product of two copositive matrices is a copositive biquadratic tensor. We then study two easily checkable subclasses of CPB tensors, namely positive biquadratic Cauchy tensors and biquadratic Pascal tensors. We show that a biquadratic Pascal tensor is both strongly CPB and positive definite.
Keywords
Cite
@article{arxiv.2510.10972,
title = {Completely Positive Biquadratic Tensors},
author = {Liqun Qi and Chunfeng Cui and Haibin Chen and Yi Xu},
journal= {arXiv preprint arXiv:2510.10972},
year = {2025}
}