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Characterization, perturbation, and interval property of certain sign regular matrices

  • The class of square matrices of order n having a negative determinant and all their minors up to order n-1 nonnegative is considered. A characterization of these matrices is presented which provides an easy test based on the Cauchon algorithm for their recognition. Furthermore, the maximum allowable perturbation of the entry in position (2,2) such that the perturbed matrix remains in this class is given. Finally, 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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Metadaten
Author:Mohammad AdmORCiDGND, Jürgen GarloffORCiDGND
URN:urn:nbn:de:bsz:kon4-opus4-29500
DOI:https://doi.org/10.1016/j.laa.2020.12.007
ISSN:0024-3795
ISSN:1873-1856
Parent Title (English):Linear Algebra and its Applications
Volume:612
Publisher:Elsevier
Document Type:Article
Language:English
Year of Publication:2021
Release Date:2022/01/08
Tag:Sign regular matrix; Totally nonnegative matrix; Interval property; Checkerboard ordering; Cauchon algorithm
First Page:146
Last Page:161
Institutes:Institut für Angewandte Forschung - IAF
DDC functional group:500 Naturwissenschaften und Mathematik
Relevance:Peer reviewed Publikation in Master Journal List
Open Access?:Nein
Licence (German):License LogoUrheberrechtlich geschützt