On the matrices related to the \(m\)-arithmetic triangle
type: Item
instance of: scholarly article
title: On the matrices related to the \(m\)-arithmetic triangle
zbMATH Open document ID: 1195.15032
author: S. Navid Salehy
author: S. Nima Salehy
author: Ali Reza Moghaddamfar
author: Seyed Majid Hosseini Pooya
published in: Linear Algebra and its Applications
publication date: 2009-12-18T00:00:00Z
review text: The authors introduce the \textit{\(m\)-arithmetic triangle} (\(m\geq 2\)) loosely speaking as follows: Starting with the entry \(1\) on the top of the triangle one defines the remaining entries as the sum of a particular choice of \(m\) elements from the previous row. For \(m=2\) this gives the well known triangle of binomial coefficients which is often attributed to Pascal. Any \(m\)-arithmetic triangle can be filled up with 0s to an infinite matrix which in turn gives rise to various (finite) submatrices. The aim of the present paper is to calculate determinants, factorisations and inverses of this kind of matrices.
reviewed by: Hans Havlicek
Mathematics Subject Classification ID: 15B36
Mathematics Subject Classification ID: 15A09
Mathematics Subject Classification ID: 11C20
Mathematics Subject Classification ID: 15A23
Mathematics Subject Classification ID: 15A15
zbMATH DE Number: 5650019
zbMATH Keywords: \(m\)-arithmetic triangle
zbMATH Keywords: Pascal's triangle
zbMATH Keywords: LU-factorisation
zbMATH Keywords: inverse matrix
zbMATH Keywords: determinants
MaRDI profile type: Publication
full work available at URL: j.laa.2009.07.006
OpenAlex ID: W2045213792
cites work: Determinants of matrices related to the Pascal triangle
cites work: Q4023405
cites work: Q4272977
cites work: Advanced determinant calculus: a complement
cites work: Pascal Matrices
cites work: Q5654049
cites work: The linear algebra of the generalized Pascal matrix
DOI: 10.1016/J.LAA.2009.07.006
description: scientific article; zbMATH DE number 5650019