TY - CHAP
U1 - Konferenzveröffentlichung
A1 - Adm, Mohammad
A1 - Garloff, Jürgen
T1 - Sign regular matrices having the interval property
T2 - Proceedings of Conference on Matrix Analysis and its Applications (MAT TRIAD 2015), Coimbra, Portugal, from 7 to 11 September 2015
N2 - We consider classes of (Formula presented.)-by-(Formula presented.) sign regular matrices, i.e. of matrices with the property that all their minors of fixed order (Formula presented.) have one specified sign or are allowed also to vanish, (Formula presented.). If the sign is nonpositive for all (Formula presented.), 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 ordering are considered. This order is obtained from the usual entry-wise ordering on the set of the (Formula presented.)-by-(Formula presented.) 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.
Y1 - 2015
UR - http://www.mattriad.ipt.pt/download/2015/Book/abstracts.pdf
SP - 169
EP - 170
ER -