Special Issue on Nonnegative matrices, M-matrices and their generalizations

Abstract

Many scientific problems which can be described by matrices, lead to structured matrices. The structure can be given for example by a specific zero pattern of the matrix, a specific pattern of the nonzero entries, a specific entry pattern, or by a specific sign pattern of the nonzero entries. The last holds for nonnegative matrices which arise e.g. in statistics, economics as well as in many areas of mathematics itself. Closely related to the class of nonnegative matrices, is the class of M-matrices whose off-diagonal entries are nonpositive. The tremendous interest in these matrices has been stimulated by their important applications. But these classes of matrices have been also fertile fields for research in their own right. During the days of November 26 and December 2, 2000 a workshop on ‘Nonnegative matrices, M-matrices and their generalizations’ took place at Mathematisches Forschungsinstitut Oberwolfach, Germany, organized by Daniel Hershkowitz, Volker Mehrmann, and Hans Schneider. The attendees were invited to submit papers to this special issue based on their presentation at the workshop. Following the Oberwolfach tradition many informal sessions were organized during the workshop. In these informal session open problems were discussed. Solutions to some of these problems are given in this special issue also. We are very grateful to all those people who contribute to the Mathematisches Forschungsinstitut Oberwolfach––a unique research place in the world.