Work

Completely Positive Biquadratic Tensors

Year: 2025

Type: preprint

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.

Source: arXiv (Cornell University)

Authors: Qi, Liqun, Cui, Chunfeng, Chen, Haibin, Xu, Yi

Institutions: Hong Kong Polytechnic University, Qufu Normal University, Southeast University

Language: English

Topic: Tensor decomposition and applications

Subfield: Computational Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funders: National Natural Science Foundation of China, Hong Kong Polytechnic University, Natural Science Foundation of Shandong Province, Fundamental Research Funds for the Central Universities

Awards: G1272805761, G2307134343, G2363803437, G290124667

OpenAlex ID: W7091187963

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