A new approach to tridiagonal matrices related to the Sylvester–Kac matrix

Efruz Özlem Mersin and Mustafa Bahşi
Notes on Number Theory and Discrete Mathematics
Print ISSN 1310–5132, Online ISSN 2367–8275
Volume 31, 2025, Number 2, Pages 211–227
DOI: 10.7546/nntdm.2025.31.2.211-227
Full paper (PDF, 307 Kb)

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Authors and affiliations

Efruz Özlem Mersin
Department of Mathematics, Faculty of Science and Arts, Aksaray University
Türkiye

Mustafa Bahşi
Department of Mathematics and Science Education, Faculty of Education, Aksaray University
Türkiye

Abstract

The Sylvester–Kac matrix, a well-known tridiagonal matrix, has been extensively studied for over a century, with various generalizations explored in the literature. This paper introduces a new type of tridiagonal matrix, where the matrix entries are defined by an integer sequence, setting it apart from the classical Sylvester–Kac matrix. The aim of this paper is to investigate several fundamental properties of this generalized matrix, including its algebraic structure, determinant, inverse, LU decomposition, characteristic polynomial, and various norms.

Keywords

• Characteristic polynomial
• Determinant
• Norm
• Sylvester–Kac matrix
• Tridiagonal matrix

2020 Mathematics Subject Classification

• 15A18
• 15A23
• 15A36
• 15A60

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Manuscript history

• Received: 28 February 2024
• Revised: 8 November 2024
• Accepted: 29 April 2025
• Online First: 5 May 2025

Copyright information

Ⓒ 2025 by the Authors.
This is an Open Access paper distributed under the terms and conditions of the Creative Commons Attribution 4.0 International License (CC BY 4.0).