Total nonnegativity of the extended Perron complement
- A real matrix is called totally nonnegative if all of its minors are nonnegative. In this paper the extended Perron complement of a principal submatrix in a matrix A is investigated. In extension of known results it is shown that if A is irreducible and totally nonnegative and the principal submatrix consists of some specified consecutive rows then the extended Perron complement is totally nonnegative. Also inequalities between minors of the extended Perron complement and the Schur complement are presented.
| Author: | Mohammad AdmORCiDGND, Jürgen GarloffORCiDGND |
|---|---|
| URL: | http://nbn-resolving.de/urn:nbn:de:bsz:352-0-386980 |
| DOI: | https://doi.org/10.1016/j.laa.2016.07.002 |
| ISSN: | 0024-3795 |
| ISSN: | 1873-1856 |
| Parent Title (English): | Linear Algebra and its Applications |
| Document Type: | Article |
| Language: | English |
| Year of Publication: | 2016 |
| Release Date: | 2019/05/16 |
| Tag: | Totally nonnegative matrix; Perron complement; Extended Perron complement; Schur complement |
| Issue: | 508 |
| First Page: | 214 |
| Last Page: | 224 |
| Open Access?: | Ja |
| Relevance: | Wiss. Zeitschriftenartikel reviewed: Listung in Positivlisten |
