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
收藏
页数：6
相关论文
共 50 条
  • [1] A Short Note on the Determinant of a Sylvester-Kac Type Matrix
    da Fonseca, Carlos M.
    INTERNATIONAL JOURNAL OF NONLINEAR SCIENCES AND NUMERICAL SIMULATION, 2020, 21 (3-4) : 361 - 362
  • [2] An observation on the determinant of a Sylvester-Kac type matrix
    da Fonseca, Carlos M.
    Kilic, Emrah
    ANALELE STIINTIFICE ALE UNIVERSITATII OVIDIUS CONSTANTA-SERIA MATEMATICA, 2020, 28 (01): : 111 - 115
  • [3] The Sylvester-Kac matrix space
    Bevilacqua, Roberto
    Bozzo, Enrico
    LINEAR ALGEBRA AND ITS APPLICATIONS, 2009, 430 (11-12) : 3131 - 3138
  • [4] A new type of Sylvester-Kac matrix and its spectrum
    da Fonseca, Carlos M.
    Kilic, Emrah
    LINEAR & MULTILINEAR ALGEBRA, 2021, 69 (06): : 1072 - 1082
  • [5] A SYLVESTER-KAC MATRIX TYPE AND THE LAPLACIAN CONTROLLABILITY OF HALF GRAPHS
    Andelic, Milica
    Da Fonseca, Carlos M.
    Kilic, Emrah
    Stanic, Zoran
    ELECTRONIC JOURNAL OF LINEAR ALGEBRA, 2022, 38 : 559 - 571
  • [6] Sylvester-Kac matrices with quadratic spectra: A comprehensive note
    Du, Zhibin
    da Fonseca, Carlos M.
    RAMANUJAN JOURNAL, 2024, 65 (03): : 1313 - 1322
  • [7] An explicit formula for singular values of the Sylvester-Kac matrix
    Boros, Tibor
    Rozsa, Pal
    LINEAR ALGEBRA AND ITS APPLICATIONS, 2007, 421 (2-3) : 407 - 416
  • [8] LEFT AND RIGHT EIGENVECTORS OF A VARIANT OF THE SYLVESTER-KAC MATRIX
    Chu, Wenchang
    Kilic, Emrah
    BULLETIN OF THE AUSTRALIAN MATHEMATICAL SOCIETY, 2024, 109 (02) : 316 - 326
  • [9] A NOTE ON THE OFF-DIAGONAL TERMS OF THE EFFECTIVE PORE DIFFUSIVITY MATRIX
    LIAPIS, AI
    LITCHFIELD, RJ
    TRANSACTIONS OF THE INSTITUTION OF CHEMICAL ENGINEERS, 1981, 59 (02): : 122 - 124
  • [10] ON THE LOCATION OF EIGENVALUES OF OFF-DIAGONAL CONSTANT MATRICES
    GENDREAU, M
    LINEAR ALGEBRA AND ITS APPLICATIONS, 1986, 79 : 99 - 102
12345