On the spectrum of tridiagonal matrices with two-periodic main diagonal

被引：0

作者：

Dyachenko, Alexander ^{[4
]}

Tyaglov, Mikhail ^{[1
,2
,3
]}

机构：

[1] St Petersburg State Univ, Dept Math & Comp Sci, St Petersburg 199178, Russia

[2] Shanghai Jiao Tong Univ, Sch Math Sci, MOE LSC, 800 Dongchuan Rd, Shanghai 200240, Peoples R China

[3] Shanghai Jiao Tong Univ, CMA Shanghai, 800 Dongchuan Rd, Shanghai 200240, Peoples R China

[4] Russian Acad Sci, Keldysh Inst Appl Math, Moscow 125047, Russia

来源：

SPECIAL MATRICES | 2024年 / 12卷 / 01期

基金：

俄罗斯科学基金会;

关键词：

tridiagonal matrices; spectrum; eigenvectors; two-periodic perturbation;

D O I：

10.1515/spma-2024-0009

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We find the spectrum and eigenvectors of an arbitrary irreducible complex tridiagonal matrix with two-periodic main diagonal. This is expressed in terms of the spectrum and eigenvectors of the matrix with the same sub- and superdiagonals and zero main diagonal. Our result generalises some recent results where the latter matrix stemmed from certain discrete orthogonal polynomials including specific cases of the classical Krawtchouk and Hahn polynomials.

引用

页数：10

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