On the spectrum of tridiagonal matrices with two-periodic main diagonal-Reference-Cited by-同舟云学术

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

Published:2024-01-01 Issue:1 Volume:12 Page:
ISSN:2300-7451
Container-title:Special Matrices
language:en
Short-container-title:

Author:

Dyachenko Alexander¹,Tyaglov Mikhail²³

Affiliation:

1. Keldysh Institute of Applied Mathematics, Russian Academy of Sciences , 125047 , Moscow , Russia

2. Department of Mathematics and Computer Sciences, St. Petersburg State University , St. Petersburg , 199178 , Russia

3. School of Mathematical Sciences, MOE-LSC, and CMA-Shanghai, Shanghai Jiao Tong University , 800 Dongchuan Road , Shanghai , 200240 , P. R. China

Abstract

Abstract 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.

Publisher

Walter de Gruyter GmbH

Link

https://www.degruyter.com/document/doi/10.1515/spma-2024-0009/pdf

Reference15 articles.

1. A. Alazemi, C. M. DaFonseca, and E. Kılıç, The spectrum of a new class of Sylvester-Kac matrices, Filomat 35 (2021), no. 12, 4017–4031.

2. R. Bronson, Matrix Methods: An Introduction, Academic Press, New York-London, 1969.

3. A. Cayley, On the determination of the value of a certain determinant, Quart. Math. J. 2 (1858), 163–166.

4. T. S. Chihara, On Kernel polynomials and related Systems, Boll. Unione Mat. Ital., III. Ser. 19 (1964), no. 4, 451–459.

5. A. Dyachenko and M. Tyaglov, Linear differential operators with polynomial coefficients generating generalised Sylvester-Kac matrices, 2021, preprint, arXiv:2104.01216.