Completion of a partial integral matrix to a unimodular matrix

Xingzhi Zhan

doi:10.1016/j.laa.2005.10.013

Completion of a partial integral matrix to a unimodular matrix

Xingzhi Zhan^*

^*此作品的通讯作者

数学科学学院

科研成果: 期刊稿件 › 文章 › 同行评审

10 引用（Scopus）

摘要

We 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.

源语言	英语
页（从-至）	373-377
页数	5
期刊	Linear Algebra and Its Applications
卷	414
期	1
DOI	https://doi.org/10.1016/j.laa.2005.10.013
出版状态	已出版 - 1 4月 2006

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AB - We 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.

KW - Completion of matrices

KW - Integral matrix

KW - Unimodular matrix

UR - https://www.scopus.com/pages/publications/33244479006

U2 - 10.1016/j.laa.2005.10.013

DO - 10.1016/j.laa.2005.10.013

M3 - 文章

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EP - 377

JO - Linear Algebra and Its Applications

JF - Linear Algebra and Its Applications

IS - 1

ER -

Completion of a partial integral matrix to a unimodular matrix

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