THE REACHABILITY CONES OF ESSENTIALLY NONNEGATIVE MATRICES by Michael Neumann * Department of Mathematics, University of Connecticut, Storrs, CT 06269–3009 and Ronald J. Stern † Department of Mathematics, Concordia University, Montreal, Canada H4X 1J7 and Michael J. Tsatsomeros ‡ Department of Mathematics, University of Connecticut, Storrs, CT 06269–3009 * Research supported in part by US Air Force Research Grant No AFOSR-88-0047 and by NSF Grant No DMS-8901860. This author would also like to thank NSERC for making it possible for him to visit Ronald J. Stern in Montreal. † Research supported by the Natural Sciences and Engineering Council of Canada, grant No A4641. ‡ Research supported in part by US Air Force Research Grant No AFOSR-88-0047 and by NSF Grant No DMS-8901860.