Year: 2014
Author: Yong Jin, Hongbo Guo
Communications in Mathematical Research , Vol. 30 (2014), Iss. 4 : pp. 289–294
Abstract
Let $h$ be a polynomial in four variables with the singular Hessian $\mathcal{H}h$ and the gradient $∇h$ and $R$ be a nonzero relation of $∇h$. Set $H = ∇R(∇h)$. We prove that the components of $H$ are linearly dependent when $rk\mathcal{H}h ≤ 2$ and give a necessary and sufficient condition for the components of $H$ to be linearly dependent when $rk\mathcal{H}h = 3$.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.13447/j.1674-5647.2014.04.01
Communications in Mathematical Research , Vol. 30 (2014), Iss. 4 : pp. 289–294
Published online: 2014-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 6
Keywords: dependence problem linear dependence quasi-translation.