@article{AdmGarloff2016,
  author    = {Adm, Mohammad and Garloff, J{\"u}rgen},
  title     = {Intervals of special sign regular matrices},
  journal   = {Linear and Multilinear Algebra},
  volume    = {64},
  number    = {7},
  issn      = {0308-1087},
  doi       = {10.1080/03081087.2015.1090388},
  pages     = {1424 -- 1444},
  year      = {2016},
  abstract  = {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.},
  language  = {de}
}