Publikation:

Matrices Having a Positive Determinant and All Other Minors Nonpositive

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2023

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Zusammenfassung

The class of square matrices of order n having a positive determinant and all their minors up to order n-1 nonpositive is considered. A characterization of these matrices based on the Cauchon algorithm is presented which provides an easy test for their recognition. Furthermore, it is shown that all matrices lying between two matrices of this class with respect to the checkerboard ordering are contained in this class, too.

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Fachgebiet (DDC)
510 Mathematik

Schlagwörter

Sign regular matrix, totally nonnegative matrix, totally nonpositive matrix, interval property, checkerboard ordering, Cauchon algorithm

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ISO 690HASSUNEH, Imad, Mohammad ADM, Jürgen GARLOFF, 2023. Matrices Having a Positive Determinant and All Other Minors Nonpositive
BibTex
@techreport{Hassuneh2023Matri-67508,
  year={2023},
  series={Konstanzer Schriften in Mathematik},
  title={Matrices Having a Positive Determinant and All Other Minors Nonpositive},
  number={410},
  author={Hassuneh, Imad and Adm, Mohammad and Garloff, Jürgen},
  note={Preprint submitted to Journal of Computational Algebra}
}
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Preprint submitted to Journal of Computational Algebra
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