Kippenhahn构造的再探讨
Kippenhahn's construction revisited
AI总结：
本文通过反例指出Kippenhahn构造在孤立奇异点失效，并利用凸几何与实代数几何完善其证明。
摘要：
Kippenhahn发现，一个复方阵的数值范围是一个平面实代数曲线的凸包。在此，我们给出一个凸集的例子，该凸集具有与数值范围类似的代数描述，然而Kippenhahn构造的类比在曲线的孤立奇异点处失效。这个例子促使我们仔细审视Kippenhahn的论断，并强调利用凸几何与实代数几何方法所获得的一个完整证明的各个方面。
英文摘要：
Kippenhahn discovered that the numerical range of a complex square matrix is the convex hull of a plane real algebraic curve. Here, we present an example of a convex set, which has a similar algebraic description as the numerical range, whereas the analogue of Kippenhahn's construction fails regarding isolated, singular points of the curve. This example prompted us to carefully review Kippenhahn's assertion and to highlight aspects of a complete proof that was achieved with methods of convex geometry and real algebraic geometry.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
