Determinants of some Hessenberg matrices with generating functions
type: Item
instance of: scholarly article
title: Determinants of some Hessenberg matrices with generating functions
zbMATH Open document ID: 1500.15003
author: Utsanee Leerawat
author: Katthaleeya Daowsud
published in: Special Matrices
publication date: 2022-09-30T00:00:00Z
review text: A lower Hessenberg matrix \(A=(a_{ij})\) is an \(n \times n\) matrix whose entries above the superdiagonal are all zero but the matrix is not lower triangular, i.e., \(a_{ij} = 0\) for all \(j>i+1\). Similarly, \(A\) is an upper Hessenberg matrix when the transpose of \(A\) is a lower Hessenberg matrix. In this paper, the generating function method is used to determine some relationships between determinants of some special lower Hessenberg matrices whose entries are terms of certain sequences, and generating functions of these sequences. These relations generalize some previous known results. Also, these relations allow one to find the determinant of many lower Hessenberg matrices
Mathematics Subject Classification ID: 15A15
Mathematics Subject Classification ID: 15B05
Mathematics Subject Classification ID: 11C20
zbMATH DE Number: 7595340
zbMATH Keywords: determinant
zbMATH Keywords: Hessenberg matrix
zbMATH Keywords: generating function
reviewed by: Julio Benítez
MaRDI profile type: Publication
full work available at URL: spma-2022-0170
OpenAlex ID: W4289517769
Wikidata QID: Q113741008
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DOI: 10.1515/SPMA-2022-0170
description: scientific article; zbMATH DE number 7595340