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Sign regular matrices having the interval property

  • 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.

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Author:Mohammad AdmORCiDGND, Jürgen GarloffORCiDGND
Parent Title (English):Proceedings of Conference on Matrix Analysis and its Applications (MAT TRIAD 2015), Coimbra, Portugal, from 7 to 11 September 2015
Document Type:Conference Proceeding
Year of Publication:2015
Release Date:2018/03/01
First Page:169
Last Page:170
Open Access?:Nein