Matrices having a positive determinant and all other minors nonpositive
The class of square matrices of order nn having a positive determinant and all their minors up to order n−1n-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...
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| Format: | Article |
| Language: | English |
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De Gruyter
2025-02-01
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| Series: | Special Matrices |
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| Online Access: | https://doi.org/10.1515/spma-2024-0031 |
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| _version_ | 1850041932645924864 |
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| author | Hassuneh Imad Adm Mohammad Garloff Jürgen |
| author_facet | Hassuneh Imad Adm Mohammad Garloff Jürgen |
| author_sort | Hassuneh Imad |
| collection | DOAJ |
| description | The class of square matrices of order nn having a positive determinant and all their minors up to order n−1n-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. For both results, we require that the entry in the bottom-right position is negative. |
| format | Article |
| id | doaj-art-6d60d68ef2f04257a1bd908db79fd20a |
| institution | DOAJ |
| issn | 2300-7451 |
| language | English |
| publishDate | 2025-02-01 |
| publisher | De Gruyter |
| record_format | Article |
| series | Special Matrices |
| spelling | doaj-art-6d60d68ef2f04257a1bd908db79fd20a2025-08-20T02:55:41ZengDe GruyterSpecial Matrices2300-74512025-02-0113124025510.1515/spma-2024-0031Matrices having a positive determinant and all other minors nonpositiveHassuneh Imad0Adm Mohammad1Garloff Jürgen2Department of Applied Mathematics and Physics, Palestine Polytechnic University, P7060796 Hebron, PalestineDepartment of Applied Mathematics and Physics, Palestine Polytechnic University, P7060796 Hebron, PalestineDepartment of Mathematics and Statistics, University of Konstanz, 78464 Konstanz, GermanyThe class of square matrices of order nn having a positive determinant and all their minors up to order n−1n-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. For both results, we require that the entry in the bottom-right position is negative.https://doi.org/10.1515/spma-2024-0031sign regular matrixtotally nonnegative matrixtotally nonpositive matrixinterval propertycheckerboard orderingcauchon algorithm15b4865g99 |
| spellingShingle | Hassuneh Imad Adm Mohammad Garloff Jürgen Matrices having a positive determinant and all other minors nonpositive Special Matrices sign regular matrix totally nonnegative matrix totally nonpositive matrix interval property checkerboard ordering cauchon algorithm 15b48 65g99 |
| title | Matrices having a positive determinant and all other minors nonpositive |
| title_full | Matrices having a positive determinant and all other minors nonpositive |
| title_fullStr | Matrices having a positive determinant and all other minors nonpositive |
| title_full_unstemmed | Matrices having a positive determinant and all other minors nonpositive |
| title_short | Matrices having a positive determinant and all other minors nonpositive |
| title_sort | matrices having a positive determinant and all other minors nonpositive |
| topic | sign regular matrix totally nonnegative matrix totally nonpositive matrix interval property checkerboard ordering cauchon algorithm 15b48 65g99 |
| url | https://doi.org/10.1515/spma-2024-0031 |
| work_keys_str_mv | AT hassunehimad matriceshavingapositivedeterminantandallotherminorsnonpositive AT admmohammad matriceshavingapositivedeterminantandallotherminorsnonpositive AT garloffjurgen matriceshavingapositivedeterminantandallotherminorsnonpositive |