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Intervals of special sign regular matrices

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https://doi.org/10.1080/03081087.2015.1090388
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Linear and Multilinear Algebra. 2016, 64(7), pp. 1424-1444. ISSN 0308-1087. eISSN 1563-5139. Available under: doi: 10.1080/03081087.2015.1090388

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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.

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510 Mathematik

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ISO 690ADM, Mohammad, Jürgen GARLOFF, 2016. Intervals of special sign regular matrices. In: Linear and Multilinear Algebra. 2016, 64(7), pp. 1424-1444. ISSN 0308-1087. eISSN 1563-5139. Available under: doi: 10.1080/03081087.2015.1090388
BibTex
@article{Adm2016-07-02Inter-31955,
  year={2016},
  doi={10.1080/03081087.2015.1090388},
  title={Intervals of special sign regular matrices},
  number={7},
  volume={64},
  issn={0308-1087},
  journal={Linear and Multilinear Algebra},
  pages={1424--1444},
  author={Adm, Mohammad and Garloff, Jürgen}
}
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