Commun. Math. Res., 30 (2014), pp. 289-294.
Published online: 2021-05
Cited by
- BibTex
- RIS
- TXT
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 $rk\mathcal{H}h = 3$.
}, issn = {2707-8523}, doi = {https://doi.org/10.13447/j.1674-5647.2014.04.01}, url = {http://global-sci.org/intro/article_detail/cmr/18953.html} }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 $rk\mathcal{H}h = 3$.