某些五对角矩阵的行列式

Pub Date : 2021-12-23 DOI:10.3336/gm.56.2.05

L. Losonczi

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引用次数: 0

摘要

本文考虑五对角线\((n+1)\times(n+1)\)矩阵，在距离主对角线\(k\)和\(2k\)处有两个次对角线和两个超对角线，其中\(1\le k \lt 2k\le n\)。我们给出了它们的行列式的显式公式，并考虑了这种矩阵的Toeplitz和“不完全”Toeplitz版本。不完美意味着主对角线的第一个和最后一个\(k\)元素与中间的元素不同。利用Egerváry和Szász的重排，我们还展示了这些决定因素是如何被分解的。

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Determinants of some pentadiagonal matrices

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 \(1\le k \lt 2k\le n\). 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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