Glasnik Matematicki, Vol. 56, No. 2 (2021), 271-286. \( \)

DETERMINANTS OF SOME PENTADIAGONAL MATRICES

László Losonczi

Faculty of Economics, University of Debrecen, 4032 Debrecen, Böszörményi u.138, Hungary
e-mail:losonczi08@gmail.com
e-mail:losonczi.laszlo@econ.unideb.hu

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.

2020 Mathematics Subject Classification.   15A15, 15B09, 15B99

Key words and phrases.   Determinants, Toeplitz matrix, pentadiagonal, tridiagonal matrices

Full text (PDF) (access from subscribing institutions only)

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

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