Matrices having a positive determinant and all other minors nonpositive
- The class of square matrices of order nhaving a positive determinant and all their minors up to order n−1nonpositive 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. For both results, we require that the entry in the bottom-right position is negative.
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| Author: | Imad Hassuneh, Mohammad AdmORCiDGND, Jürgen GarloffORCiDGND |
|---|---|
| URN: | urn:nbn:de:bsz:kon4-opus4-56064 |
| DOI: | https://doi.org/10.1515/spma-2024-0031 |
| ISSN: | 2300-7451 |
| Parent Title (English): | Special Matrices |
| Volume: | 13 |
| Publisher: | De Gruyter |
| Place of publication: | Warsaw |
| Document Type: | Article |
| Language: | English |
| Year of Publication: | 2025 |
| Release Date: | 2025/03/04 |
| Tag: | Sign regular matrix; Totally nonnegative matrix; Totally nonpositive matrix; Interval property; Checkerboard ordering; Cauchon algorithm |
| Issue: | 1 |
| Page Number: | 21 |
| Article Number: | 20240031 |
| DDC functional group: | 500 Naturwissenschaften und Mathematik |
| Open Access?: | Ja |
| Relevance: | Wiss. Zeitschriftenartikel reviewed: Listung in Positivlisten |
| Licence (German): |  Creative Commons - CC BY - Namensnennung 4.0 International |
