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%Noutsos
%Dimitrios","dnoutsos@uoi.gr","
\section*{Reachability cone of eventually exponentially nonnegative matrices} By {\sl Dimitrios Noutsos and Michael Tsatsomeros}.  

\medskip  \noindent We examine the relation between eventual exponential nonnegativity of a matrix $A$ ($e^{tA}\geq 0$ for all sufficiently large $t\geq 0$) and eventual nonnegativity of $I+hA, ~ h\geq 0$ ($(I+hA)^k\geq 0$ for all sufficiently large $k\geq 0$). As a consequence, we are able to characterize initial points $x_0\in \mathbb{R}^n$ such that $e^{tA}x_0$ becomes and remains nonnegative as exactly those points for which the discrete trajectories $x^{(k)} = (I+hA)^kx_0$ become and remain nonnegative. This extents work on the reachability cone of exponentially nonnegative matrices by Neumann, Stern and Tsatsomeros [1].   

\bigskip \noindent
 [1] M. Neumann, R.J. Stern, and M. Tsatsomeros. The reachability cones of essentially nonnegative matrices. {\em Linear and Multilinear Algebra}, 28:213--224, 1991.
%Eventually nonnegative matrix; eventually exponentially nonnegative matrix; point of nonnegative potential; reachability cone","15A48","65F10","Consider my talk for the mini-simposium ""MS8 Nonnegative and eventually nonnegative matrices"", organized by Judi McDonald","16:19:05","Mon Mar 31 2008","134.121.45.4"


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