论文标题
可对角矩阵和双schoenberg类型不平等的整合性
Integrability of diagonalizable matrices and a dual Schoenberg type inequality
论文作者
论文摘要
引入了矩阵的分化和整合概念，用于研究复杂多项式的零点和临界点。任何矩阵都是可区分的，但是并非所有矩阵都是可以集成的。本文的目的是研究可集成性属性，并在可对角矩阵的类别中表征它。为此，我们研究了可对角矩阵的光谱之间的关系及其积分性和积分的对角线性之间的关系。最后，我们运用结果来获得双重的Schoenberg类型不等式，将多项式的零与其临界点有关。
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.
