论文标题
有关关键点位置的某些经典结果的母系证明
Matricial Proofs of Some Classical Results about Critical Point Location
论文作者
论文摘要
高斯 - 卢卡斯（Lucas）和bôcher-grace-遵守定理是多项式几何形状的经典结果。这些结果的证据在文献中可以使用，但方法似乎有所不同。在这项工作中，我们表明可以在使用矩阵分析的统一理论框架中证明这些定理（尤其是使用值和矩阵的差异化）。此外，由于Siebeck，我们还提供了众所周知的结果的有用变体。
The Gauss--Lucas and Bôcher--Grace--Marden theorems are classical results in the geometry of polynomials. Proofs of the these results are available in the literature, but the approaches are seemingly different. In this work, we show that these theorems can be proven in a unified theoretical framework utilizing matrix analysis (in particular, using the field of values and the differentiator of a matrix). In addition, we provide a useful variant of a well-known result due to Siebeck.
