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Glasnik matematički, Vol. 56 No. 2, 2021.

Original scientific paper

https://doi.org/10.3336/gm.56.2.05

Determinants of some pentadiagonal matrices

László Losonczi ; Faculty of Economics, University of Debrecen, 4032 Debrecen, Böszörményi u.138, Hungary

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Abstract

In this paper we consider pentadiagonal \((n+1)\times(n+1)\) matrices with two subdiagonals and two superdiagonals at distances \(k\) and \(2k\) from the main diagonal where \(1\le k < 2k\le n\). We give an explicit formula for their determinants and also consider the Toeplitz and “imperfect” Toeplitz versions of such matrices. Imperfectness means that the first and last \(k\) elements of the main diagonal differ from the elements in the middle. Using the rearrangement due to Egerváry and Szász we also show how these determinants can be factorized.

Keywords

Determinants, Toeplitz matrix, pentadiagonal, tridiagonal matrices

Hrčak ID:

267563

URI

https://hrcak.srce.hr/267563

Publication date:

23.12.2021.

Visits: 460 *

Publication date: 31 December 2021

Volume: Vol 56

Issue: Svezak 2

Pages: 271-286

DOI: https://doi.org/10.3336/gm.56.2.05

Article Information (continued)

Categories:

Subject: Izvorni znanstveni članak

Keywords:

Keyword: Determinants, Toeplitz matrix, pentadiagonal, tridiagonal matrices

Determinants of some pentadiagonal matrices

László Losonczi[1]

Email: losonczi08@gmail.com

 

[1] Faculty of Economics, University of Debrecen, 4032 Debrecen, Böszörményi u.138, Hungary

Abstract

In this paper we consider pentadiagonal \((n+1)\times(n+1)\) matrices with two subdiagonals and two superdiagonals at distances \(k\) and \(2k\) from the main diagonal where \(1\le k < 2k\le n\). We give an explicit formula for their determinants and also consider the Toeplitz and “imperfect” Toeplitz versions of such matrices. Imperfectness means that the first and last \(k\) elements of the main diagonal differ from the elements in the middle. Using the rearrangement due to Egerváry and Szász we also show how these determinants can be factorized.

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