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.