Completion of a partial integral matrix to a unimodular matrix
type: Item
instance of: scholarly article
title: Completion of a partial integral matrix to a unimodular matrix
zbMATH Open document ID: 1090.15013
author: Xingzhi Zhan
published in: Linear Algebra and its Applications
publication date: 2006-03-29T00:00:00Z
review text: The paper deals with unimodular matrix completion problem, that is, when a partial integral matrix has a unimodular matrix completion. Given an \(n \times n\) integral unimodular matrix \(A\), the author characterizes submatrices of \(A\) via the number of invariant factors equal to 1. By using the above characterization, he proves that if \(n\) entries of an \(n \times n\) partial integral matrix are prescribed and these entries do not constitute a row or a column, then this matrix can be completed to a unimodular matrix. As a trivial consequence, every \(n \times n\) partial integral matrix with \(n-1\) prescribed entries has a unimodular matrix completion.
Mathematics Subject Classification ID: 15A29
Mathematics Subject Classification ID: 15B36
Mathematics Subject Classification ID: 11C20
zbMATH DE Number: 5016239
zbMATH Keywords: Partial matrix
zbMATH Keywords: integral matrix
zbMATH Keywords: unimodular matrix completion problem
reviewed by: Juan Ramón Torregrosa Sánchez
MaRDI profile type: Publication
full work available at URL: j.laa.2005.10.013
OpenAlex ID: W2147159947
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DOI: 10.1016/J.LAA.2005.10.013
description: scientific article; zbMATH DE number 5016239