On Separation of level sets for a pair of quadratic functions

• Published in: arXiv.org
• Main Authors: Nguyen, Huu-Quang, Ya-Chi Chu, Ruey-Lin Sheu
• Format: Paper
• Language: English
• Published: Ithaca Cornell University Library, arXiv.org 13.01.2021
• Subjects: Quadratic equations

Given a quadratic function \(f(x)=x^TAx+2a^Tx+a_0,\) it is possible that its level set \(\{x\in\mathbb{R}^n: f(x)=0\}\) has two connected components and thus can be separated by the level set \(\{x\in\mathbb{R}^n: g(x)=0\}\) of another quadratic function \(g(x)=x^TBx+2b^Tx+b_0.\) It turns out that t...