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^*

^*Corresponding author for this work

School of Mathematical Sciences

Research output: Contribution to journal › Article › peer-review

10 Scopus citations

Abstract

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.

Original language	English
Pages (from-to)	373-377
Number of pages	5
Journal	Linear Algebra and Its Applications
Volume	414
Issue number	1
DOIs	https://doi.org/10.1016/j.laa.2005.10.013
State	Published - 1 Apr 2006

Keywords

Completion of matrices
Integral matrix
Unimodular matrix

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10.1016/j.laa.2005.10.013

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title = "Completion of a partial integral matrix to a unimodular matrix",

abstract = "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.",

keywords = "Completion of matrices, Integral matrix, Unimodular matrix",

author = "Xingzhi Zhan",

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AU - Zhan, Xingzhi

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N2 - 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.

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

AN - SCOPUS:33244479006

SN - 0024-3795

VL - 414

SP - 373

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

Abstract

Keywords

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