Inertia sets allowed by matrix patterns
Motivated by the possible onset of instability in dynamical systems associated with a zero eigenvalue, sets of inertias $\sn_n$ and $\SN{n}$ for sign and zero-nonzero patterns, respectively, are introduced. For an $n\times n$ sign pattern $\mc{A}$ that allows inertia $(0,n-1,1)$, a sufficient condit...
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Veröffentlicht in: | Electronic Journal of Linear Algebra 2018-08, Vol.34 (1) |
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creator | Berliner, Adam H Olesky, Dale D van den Driessche, Pauline |
description | Motivated by the possible onset of instability in dynamical systems associated with a zero eigenvalue, sets of inertias $\sn_n$ and $\SN{n}$ for sign and zero-nonzero patterns, respectively, are introduced. For an $n\times n$ sign pattern $\mc{A}$ that allows inertia $(0,n-1,1)$, a sufficient condition is given for $\mc{A}$ and every superpattern of $\mc{A}$ to allow $\sn_n$, and a family of such irreducible sign patterns for all $n\geq 3$ is specified. All zero-nonzero patterns (up to equivalence) that allow $\SN{3}$ and $\SN{4}$ are determined, and are described by their associated digraphs. |
doi_str_mv | 10.13001/1081-3810,1537-9582.3647 |
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For an $n\times n$ sign pattern $\mc{A}$ that allows inertia $(0,n-1,1)$, a sufficient condition is given for $\mc{A}$ and every superpattern of $\mc{A}$ to allow $\sn_n$, and a family of such irreducible sign patterns for all $n\geq 3$ is specified. 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For an $n\times n$ sign pattern $\mc{A}$ that allows inertia $(0,n-1,1)$, a sufficient condition is given for $\mc{A}$ and every superpattern of $\mc{A}$ to allow $\sn_n$, and a family of such irreducible sign patterns for all $n\geq 3$ is specified. All zero-nonzero patterns (up to equivalence) that allow $\SN{3}$ and $\SN{4}$ are determined, and are described by their associated digraphs.</description><issn>1081-3810</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2018</creationdate><recordtype>article</recordtype><sourceid/><recordid>eNqFjbsKwkAQAA9BMD5-Qc7KxsTdXGLOWhTT24cNrhC5xHB7oPl7EcTWaooZGKVWCAkaANwiWIyNRdhgbop4n9s0MbusGKnopyZqKnIHSCGzeaTWZcc-NKSFg2hy7vHkq64H3VLwzUv3FAL7TuZqfCMnvPhyppan4-VwjmvuPYtUvW9a8kPFjj5L8zd4A6ZfM-k</recordid><startdate>20180805</startdate><enddate>20180805</enddate><creator>Berliner, Adam H</creator><creator>Olesky, Dale D</creator><creator>van den Driessche, Pauline</creator><general>University of Wyoming</general><scope/></search><sort><creationdate>20180805</creationdate><title>Inertia sets allowed by matrix patterns</title><author>Berliner, Adam H ; Olesky, Dale D ; van den Driessche, Pauline</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-bepress_primary_ela36473</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><creationdate>2018</creationdate><toplevel>online_resources</toplevel><creatorcontrib>Berliner, Adam H</creatorcontrib><creatorcontrib>Olesky, Dale D</creatorcontrib><creatorcontrib>van den Driessche, Pauline</creatorcontrib><jtitle>Electronic Journal of Linear Algebra</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Berliner, Adam H</au><au>Olesky, Dale D</au><au>van den Driessche, Pauline</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Inertia sets allowed by matrix patterns</atitle><jtitle>Electronic Journal of Linear Algebra</jtitle><date>2018-08-05</date><risdate>2018</risdate><volume>34</volume><issue>1</issue><eissn>1081-3810</eissn><abstract>Motivated by the possible onset of instability in dynamical systems associated with a zero eigenvalue, sets of inertias $\sn_n$ and $\SN{n}$ for sign and zero-nonzero patterns, respectively, are introduced. For an $n\times n$ sign pattern $\mc{A}$ that allows inertia $(0,n-1,1)$, a sufficient condition is given for $\mc{A}$ and every superpattern of $\mc{A}$ to allow $\sn_n$, and a family of such irreducible sign patterns for all $n\geq 3$ is specified. All zero-nonzero patterns (up to equivalence) that allow $\SN{3}$ and $\SN{4}$ are determined, and are described by their associated digraphs.</abstract><pub>University of Wyoming</pub><doi>10.13001/1081-3810,1537-9582.3647</doi></addata></record> |
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title | Inertia sets allowed by matrix patterns |
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