Determinants of some pentadiagonal matrices

Abstract

In this paper we consider pentadiagonal (n + 1) × (n + 1) matrices with two subdiagonals and two superdiagonals at distances k and 2k from the main diagonal where 1 ≤ k < 2k ≤ 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.