A note on the eigenvalues of a Sylvester-Kac type matrix with off-diagonal biperiodic perturbations

被引：0

作者：

Du, Zhibin ^{[1
]}

da Fonseca, Carlos M. ^{[2
,3
,4
]}

机构：

[1] South China Normal Univ, Sch Artificial Intelligence, Foshan 528225, Guangdong, Peoples R China

[2] Kuwait Coll Sci & Technol, Safat 13133, Kuwait

[3] Tech Univ Sofia, Fac Appl Math & Informat, Kliment Ohridski Blvd 8, Sofia 1000, Bulgaria

[4] Univ Deusto, Chair Computat Math, Bilbao 48007, Spain

来源：

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS | 2025年 / 461卷

关键词：

Sylvester-Kac matrix; Tridiagonal matrix; Eigenvalues; TRIDIAGONAL MATRICES; EIGENVECTORS; DETERMINANT; PROPERTY; SPECTRUM; VALUES;

D O I：

10.1016/j.cam.2024.116429

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The Sylvester-Kac matrix is a tridiagonal matrix with integer entries having a certain kind of regular pattern. Its eigenvalues and eigenvectors can be computed analytically, so it can be used for test matrices for eigenvalue solvers. Among the extensions of the Sylvester-Kac matrix, one of the most challenging is when a given constant is added biperiodically to the non-zero off- diagonal entries. In this note we provide a combinatorial proof for determining the eigenvalues of such matrices. We also discuss a possible biperiodic extension.

引用

页数：6

共 43 条

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