Intervals of special sign regular matrices
- We consider classes of n-by-n sign regular matrices, i.e., of matrices with the property that all their minors of fixed order k have one specified sign or are allowed also to vanish, k = 1, ... ,n. If the sign is nonpositive for all k, such a matrix is called totally nonpositive. The application of the Cauchon algorithm to nonsingular totally nonpositive matrices is investigated and a new determinantal test for these matrices is derived. Also matrix intervals with respect to the checkerboard partial ordering are considered. This order is obtained from the usual entry-wise ordering on the set of the n-by-n matrices by reversing the inequality sign for each entry in a checkerboard fashion. For some classes of sign regular matrices it is shown that if the two bound matrices of such a matrix interval are both in the same class then all matrices lying between these two bound matrices are in the same class, too.
| Author: | Mohammad AdmORCiDGND, Jürgen GarloffORCiDGND |
|---|---|
| DOI: | https://doi.org/10.1080/03081087.2015.1090388 |
| ISSN: | 0308-1087 |
| Parent Title (German): | Linear and Multilinear Algebra |
| Volume: | 64 |
| Document Type: | Article |
| Language: | German |
| Year of Publication: | 2016 |
| Release Date: | 2019/05/16 |
| Tag: | Sign regular matrix; Totally nonnegative matrix; Totally nonpositve matrix; Cauchon algorithm; Checkerboard ordering |
| Issue: | 7 |
| First Page: | 1424 |
| Last Page: | 1444 |
| Relevance: | Wiss. Zeitschriftenartikel reviewed: Listung in Positivlisten |
| Open Access?: | Nein |
