关于一些具有Kippenhahn曲线椭圆分量的倒易矩阵

IF 0.8 Q2 MATHEMATICS

Special Matrices Pub Date : 2021-12-07 DOI:10.1515/spma-2021-0151

Muyan Jiang, I. Spitkovsky

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引用次数: 1

摘要

摘要根据定义，互反矩阵是具有恒定主对角线的三对角n × n矩阵A，且使得ai,i+1ai+1，对于i= 1，…，n−1,i= 1。我们建立了这类矩阵的数值范围生成曲线C(A)(也称为Kippenhahn曲线)的一些性质，特别是关于其椭圆分量的位置。特别是当n≤6时，我们完整地描述了C(A)完全由椭圆组成的情况。作为推论，当满足这些条件时，我们还提供了更高阶数值范围的完整描述。

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On some reciprocal matrices with elliptical components of their Kippenhahn curves

Abstract By definition, reciprocal matrices are tridiagonal n-by-n matrices A with constant main diagonal and such that ai,i+1ai+1,i= 1 for i = 1, . . ., n − 1. We establish some properties of the numerical range generating curves C(A) (also called Kippenhahn curves) of such matrices, in particular concerning the location of their elliptical components. For n ≤ 6, in particular, we describe completely the cases when C(A) consist entirely of ellipses. As a corollary, we also provide a complete description of higher rank numerical ranges when these criteria are met.

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来源期刊

Special Matrices MATHEMATICS-

CiteScore

1.10

自引率

20.00%

发文量

审稿时长

8 weeks

期刊介绍： Special Matrices publishes original articles of wide significance and originality in all areas of research involving structured matrices present in various branches of pure and applied mathematics and their noteworthy applications in physics, engineering, and other sciences. Special Matrices provides a hub for all researchers working across structured matrices to present their discoveries, and to be a forum for the discussion of the important issues in this vibrant area of matrix theory. Special Matrices brings together in one place major contributions to structured matrices and their applications. All the manuscripts are considered by originality, scientific importance and interest to a general mathematical audience. The journal also provides secure archiving by De Gruyter and the independent archiving service Portico.