TY  - JOUR
U1  - Zeitschriftenartikel, wissenschaftlich - begutachtet (reviewed)
A1  - Adm, Mohammad
A1  - Garloff, Jürgen
T1  - Intervals of special sign regular matrices
JF  - Linear and Multilinear Algebra
N2  - 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.
KW  - Sign regular matrix
KW  - Totally nonnegative matrix
KW  - Totally nonpositve matrix
KW  - Cauchon algorithm
KW  - Checkerboard ordering
Y1  - 2016
SN  - 0308-1087
SS  - 0308-1087
U6  - https://doi.org/10.1080/03081087.2015.1090388
DO  - https://doi.org/10.1080/03081087.2015.1090388
VL  - 64
IS  - 7
SP  - 1424
EP  - 1444
ER  -