正规矩阵的谱逆问题及Gauss-Lucas定理的推广
Inverse spectral problem for normal matrices and a generalization of the Gauss-Lucas theorem
摘要：
利用优化方法建立了正规矩阵的Cauchy-Poincare分离定理的一个类似定理。此外，我们提出了一个解决方案的逆谱问题（Borg型结果）的正规矩阵。利用这一结果，我们基本上推广和补充已知的高斯-卢卡斯定理的几何根的一个复杂的多项式及其衍生物。最后一个结果又用来证明de Bruijn-Springer和Schoenberg关于这些根的旧命题。
英文摘要：
We estabish an analog of the Cauchy-Poincare separation theorem for normal matrices in terms of majorization. Moreover, we present a solution to the inverse spectral problem (Borg-type result) for a normal matrix. Using this result we essentially generalize and complement the known Gauss--Lucas theorem on the geometry of the roots of a complex polynomial and of its derivative. In turn the last result is applied to prove the old conjectures of de Bruijn-Springer and Schoenberg about these roots.
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