Intervals of Special Sign Regular Matrices

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ADM, Mohammad, Jürgen GARLOFF, 2015. Intervals of Special Sign Regular Matrices. Available under: doi: 10.1080/03081087.2015.1090388

@techreport{Adm2015Inter-31960, series={Konstanzer Schriften in Mathematik}, title={Intervals of Special Sign Regular Matrices}, year={2015}, doi={10.1080/03081087.2015.1090388}, number={341}, author={Adm, Mohammad and Garloff, Jürgen}, note={Der Artikel wird erscheinen in: "Linear and Multilinear Algebra"} }

<rdf:RDF xmlns:dcterms="" xmlns:dc="" xmlns:rdf="" xmlns:bibo="" xmlns:dspace="" xmlns:foaf="" xmlns:void="" xmlns:xsd="" > <rdf:Description rdf:about=""> <dc:creator>Garloff, Jürgen</dc:creator> <dc:contributor>Adm, Mohammad</dc:contributor> <void:sparqlEndpoint rdf:resource="http://localhost/fuseki/dspace/sparql"/> <dc:date rdf:datatype="">2015-10-16T12:06:31Z</dc:date> <dc:creator>Adm, Mohammad</dc:creator> <dcterms:available rdf:datatype="">2015-10-16T12:06:31Z</dcterms:available> <dcterms:isPartOf rdf:resource=""/> <dc:language>eng</dc:language> <bibo:uri rdf:resource=""/> <dc:contributor>Garloff, Jürgen</dc:contributor> <dspace:isPartOfCollection rdf:resource=""/> <dcterms:rights rdf:resource=""/> <foaf:homepage rdf:resource="http://localhost:8080/jspui"/> <dcterms:issued>2015</dcterms:issued> <dcterms:abstract xml:lang="eng">We consider classes of n-by-n sign regular matrices, i.e., of matrices with the property that all their minors of fixed order k have one specified sign or are allowed also to vanish, k = 1, ... ,n. If the sign is nonpositive for all k, such a matrix is called totally nonpositive. The application of the Cauchon algorithm to nonsingular totally nonpositive matrices is investigated and a new determinantal test for these matrices is derived. Also matrix intervals with respect to the checkerboard partial ordering are considered. This order is obtained from the usual entry-wise ordering on the set of the n-by-n matrices by reversing the inequality sign for each entry in a checkerboard fashion. For some classes of sign regular matrices it is shown that if the two bound matrices of such a matrix interval are both in the same class then all matrices lying between these two bound matrices are in the same class, too.</dcterms:abstract> <dspace:hasBitstream rdf:resource=""/> <dcterms:title>Intervals of Special Sign Regular Matrices</dcterms:title> <dc:rights>terms-of-use</dc:rights> <dcterms:hasPart rdf:resource=""/> </rdf:Description> </rdf:RDF>

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