Type of Publication:  Journal article 
Author:  Adm, Mohammad; Garloff, Jürgen 
Year of publication:  2016 
Published in:  Linear and Multilinear Algebra ; 64 (2016), 7.  pp. 14241444.  ISSN 03081087.  eISSN 15635139 
DOI (citable link):  https://dx.doi.org/10.1080/03081087.2015.1090388 
Summary: 
We consider classes of nbyn 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 entrywise ordering on the set of the nbyn 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.

Subject (DDC):  510 Mathematics 
Bibliography of Konstanz:  Yes 
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ADM, Mohammad, Jürgen GARLOFF, 2016. Intervals of special sign regular matrices. In: Linear and Multilinear Algebra. 64(7), pp. 14241444. ISSN 03081087. eISSN 15635139. Available under: doi: 10.1080/03081087.2015.1090388
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