主次映射的纤维及其在稳定多项式中的应用

IF 0.8 2区 数学 Q2 MATHEMATICS
Abeer Al Ahmadieh
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引用次数: 0

摘要

本文探讨了任意场上主次映射的纤维。主次映射将其主次映射的2n向量分配给每个n×n矩阵。1984年,hartfield和Loewy提出了一个足以保证主副映射的光纤是单点直至对角等价的条件。洛伊后来在1986年对这种情况进行了改进。本文给出了光纤达到对角等价的一个充要条件。此外,我们建立了矩阵的可约性与其行列式表示的可约性之间的联系。利用这种联系,我们在任意场上的n×n矩阵空间中完整地描述了包含对称矩阵或厄米矩阵的光纤。我们还使用这些技术来回答Borcea, Brändén和Liggett关于实稳定矩阵的问题。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
On the fibers of the principal minor map and an application to stable polynomials
This paper explores the fibers of the principal minor map over an arbitrary field. The principal minor map assigns to each n×n matrix the 2n-vector of its principal minors. In 1984, Hartfiel and Loewy proposed a condition that was sufficient to ensure that the fiber of the principal minor map is a single point up to diagonal equivalence. Loewy later improved upon this condition in 1986. In this paper, we provide a necessary and sufficient condition for the fiber to be a point up to diagonal equivalence. Additionally, we establish a connection between the reducibility of a matrix and the reducibility of its determinantal representation. Using this connection, we fully characterize the fibers that contain a symmetric or Hermitian matrix in the space of n×n matrices over any field. We also use these techniques to answer a question of Borcea, Brändén, and Liggett concerning real stable matrices.
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来源期刊
Journal of Algebra
Journal of Algebra 数学-数学
CiteScore
1.50
自引率
22.20%
发文量
414
审稿时长
2-4 weeks
期刊介绍: The Journal of Algebra is a leading international journal and publishes papers that demonstrate high quality research results in algebra and related computational aspects. Only the very best and most interesting papers are to be considered for publication in the journal. With this in mind, it is important that the contribution offer a substantial result that will have a lasting effect upon the field. The journal also seeks work that presents innovative techniques that offer promising results for future research.
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