可对角化矩阵的可积性与一个对偶Schoenberg型不等式
Integrability of diagonalizable matrices and a dual Schoenberg type inequality
摘要：
为了研究复多项式的零点和临界点，引入了矩阵微分和积分的概念。任何矩阵都是可微的，但并非所有矩阵都是可积的。本文的目的是研究可对角化矩阵类的可积性，并刻画它。为此，我们研究了可对角化矩阵的谱与其可积性和积分的可对角化性之间的关系。最后，我们应用所得结果得到了一个关于多项式零点与其临界点的对偶Schoenberg型不等式。
英文摘要：
The concepts of differentiation and integration for matrices were introduced for studying zeros and critical points of complex polynomials. Any matrix is differentiable, however not all matrices are integrable. The purpose of this paper is to investigate the integrability property and characterize it within the class of diagonalizable matrices. In order to do this we study the relation between the spectrum of a diagonalizable matrix and its integrability and the diagonalizability of the integral. Finally, we apply our results to obtain a dual Schoenberg type inequality relating zeros of polynomials with their critical points.
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