Intervals of Special Sign Regular Matrices

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2015
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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.

Zusammenfassung in einer weiteren Sprache
Fachgebiet (DDC)
510 Mathematik
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Sign regular matrix, totally nonnegative matrix, totally nonpositve matrix, Cauchon algorithm, checkerboard ordering, matrix interval
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ISO 690ADM, Mohammad, Jürgen GARLOFF, 2015. Intervals of Special Sign Regular Matrices
BibTex
@techreport{Adm2015Inter-31960,
  year={2015},
  doi={10.1080/03081087.2015.1090388},
  series={Konstanzer Schriften in Mathematik},
  title={Intervals of Special Sign Regular Matrices},
  number={341},
  author={Adm, Mohammad and Garloff, Jürgen},
  note={Der Artikel wird erscheinen in: "Linear and Multilinear Algebra"}
}
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Der Artikel wird erscheinen in: "Linear and Multilinear Algebra"
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