On the <i>Z<sub>n</sub></i> sign pattern matrices

On the <i>Z<sub>n</sub></i> sign pattern matrices

Let <i>Z<sub>n</sub></i> dente the set of all square sign pattern matrices of order <i>n</i> whose off-diagonal entries are non-positive.For a sign pattern matrix <i>A</i>∈<i>Z<sub>n</sub></i> and two arbitrary real matrices <...

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Bibliographic Details
Main Authors: FANG Maozhong, ZHANG Jizhou
Format: Article
Language:English
Published: Academic Journals Center of Shanghai Normal University 2013-12-01
Series:Journal of Shanghai Normal University (Natural Sciences)
Subjects:
sign pattern matrix
closure
reducible
Online Access:http://qktg.shnu.edu.cn/zrb/shsfqkszrb/ch/reader/create_pdf.aspx?file_no=201306003&year_id=2013&quarter_id=6&falg=1
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spelling doaj-cbc7ce2111444dbcadf3c8cabb6c5f252020-11-24T20:59:35ZengAcademic Journals Center of Shanghai Normal UniversityJournal of Shanghai Normal University (Natural Sciences)1000-51371000-51372013-12-01426580583201306003On the <i>Z<sub>n</sub></i> sign pattern matricesFANG Maozhong0ZHANG Jizhou1School of Mathematics and Information,Shanghai Lixin University of CommerceCollege of Mathematics and Sciences,Shanghai Normal UniversityLet <i>Z<sub>n</sub></i> dente the set of all square sign pattern matrices of order <i>n</i> whose off-diagonal entries are non-positive.For a sign pattern matrix <i>A</i>∈<i>Z<sub>n</sub></i> and two arbitrary real matrices <i>B</i><sub>1</sub>,<i>B</i><sub>2</sub> with sign pattern <i>A</i>,if sgn(<i>B</i><sub>1</sub><i>B</i><sub>2</sub>)∈<i>Z<sub>n</sub></i>,then we call this property the closure property of <i>Z<sub>n</sub></i>.We prove that if <i>A</i>∈<i>Z<sub>n</sub></i>(<i>n</i>≥3) and <i>A</i> has the closure property of <i>Z<sub>n</sub></i>,then <i>A</i> must be reducible.We also characterize this kind of <i>Z<sub>n</sub></i> sign pattern matrices.http://qktg.shnu.edu.cn/zrb/shsfqkszrb/ch/reader/create_pdf.aspx?file_no=201306003&year_id=2013&quarter_id=6&falg=1sign pattern matrixclosurereducible
collection DOAJ
language English
format Article
sources DOAJ
author FANG Maozhong
ZHANG Jizhou
spellingShingle FANG Maozhong
ZHANG Jizhou
On the <i>Z<sub>n</sub></i> sign pattern matrices
Journal of Shanghai Normal University (Natural Sciences)
sign pattern matrix
closure
reducible
author_facet FANG Maozhong
ZHANG Jizhou
author_sort FANG Maozhong
title On the <i>Z<sub>n</sub></i> sign pattern matrices
title_short On the <i>Z<sub>n</sub></i> sign pattern matrices
title_full On the <i>Z<sub>n</sub></i> sign pattern matrices
title_fullStr On the <i>Z<sub>n</sub></i> sign pattern matrices
title_full_unstemmed On the <i>Z<sub>n</sub></i> sign pattern matrices
title_sort on the <i>z<sub>n</sub></i> sign pattern matrices
publisher Academic Journals Center of Shanghai Normal University
series Journal of Shanghai Normal University (Natural Sciences)
issn 1000-5137
1000-5137
publishDate 2013-12-01
description Let <i>Z<sub>n</sub></i> dente the set of all square sign pattern matrices of order <i>n</i> whose off-diagonal entries are non-positive.For a sign pattern matrix <i>A</i>∈<i>Z<sub>n</sub></i> and two arbitrary real matrices <i>B</i><sub>1</sub>,<i>B</i><sub>2</sub> with sign pattern <i>A</i>,if sgn(<i>B</i><sub>1</sub><i>B</i><sub>2</sub>)∈<i>Z<sub>n</sub></i>,then we call this property the closure property of <i>Z<sub>n</sub></i>.We prove that if <i>A</i>∈<i>Z<sub>n</sub></i>(<i>n</i>≥3) and <i>A</i> has the closure property of <i>Z<sub>n</sub></i>,then <i>A</i> must be reducible.We also characterize this kind of <i>Z<sub>n</sub></i> sign pattern matrices.
topic sign pattern matrix
closure
reducible
url http://qktg.shnu.edu.cn/zrb/shsfqkszrb/ch/reader/create_pdf.aspx?file_no=201306003&year_id=2013&quarter_id=6&falg=1
work_keys_str_mv AT fangmaozhong ontheizsubnsubisignpatternmatrices
AT zhangjizhou ontheizsubnsubisignpatternmatrices
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