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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.

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Author:Mohammad AdmORCiDGND, Jürgen GarloffORCiDGND
Parent Title (German):Linear and Multilinear Algebra
Document Type:Article
Year of Publication:2016
Release Date:2019/05/16
Tag:Sign regular matrix; Totally nonnegative matrix; Totally nonpositve matrix; Cauchon algorithm; Checkerboard ordering
First Page:1424
Last Page:1444
Relevance:Peer reviewed Publikation in Master Journal List
Open Access?:Nein