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Completion of a partial integral matrix to a unimodular matrix

By Xingzhi Zhan

Abstract

AbstractWe first characterize submatrices of a unimodular integral matrix. We then prove that if n entries of an n×n partial integral matrix are prescribed and these n entries do not constitute a row or a column, then this matrix can be completed to a unimodular matrix. Consequently an n×n partial integral matrix with n−1 prescribed entries can always be completed to a unimodular matrix

Publisher: Elsevier Inc.
Year: 2006
DOI identifier: 10.1016/j.laa.2005.10.013
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