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%Maroulas
%John","maroulas@math.ntua.gr","
\section{Dilation of numerical ranges  of normal matrices} By {\sl Maria Adam and John Maroulas}.  

\medskip  \noindent Let $\,A\,$ be an $\,n \times n\,$ normal matrix, whose the numerical range $\,NR[A]\,$ is a $\,k-$polygon, and let $\,v \in \mathbb{C}^{n},\,$ be a unit vector. If for a unit vector $\,v \in \mathbb{C}^{n},\,$ the point $\,v^{*}Av\,$ is interior point of $\,NR[A]\,$ and $\,P\,$ is an $\,n \times (k-1)\,$ matrix, such that $\,P^{*}P=I_{k-1}\,$ and $\,v \bot ImP, \,$ then $\,NR[A]\,$ is circumscribed to $\,NR[C],\,$ where $\,C=P^{*}AP .$  In this paper, we investigate the converse way, showing how we obtain $\,NR[A],\,$ from a $\,(k-1)-$polygon, such that the boundary of $\,NR[C]\,$ shares the same tangential points with the sides of both polygons.
%compression;eigenvalue;numerical range","15A60","15A18","","04:06:52","Mon Feb 04 2008","85.75.27.34"
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