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%"Sendov","Hristo","hssendov@stats.uwo.ca","
\section*{Spectral Manifolds} By {\sl A. Daniilidis, J. Malick, A. Lewis, H.S. Sendov$^*$}.  

\medskip \noindent 
It is well known that the set of all $n \times n$ symmetric matrices of rank $k$ is a smooth manifold. This set can be described as those symmetric matrices whose ordered vector of eigenvalues has exactly $n-k$ zeros. The set of all vectors in $\R^n$ with exactly $n-k$ zero entries is itself an analytic manifold.   In this work, we characterize the manifolds $M$ in $\R^n$ with the property that the set of all $n \times n$ symmetric matrices whose ordered vector of eigenvalues belongs to $M$ is a manifold. In particular, we show that if $M$ is a $C^2$, $C^{\infty}$, or $C^{\omega}$ manifold then so is the corresponding matrix set. We give a formula for the dimension of the matrix manifold in terms of the dimension of $M$.

%","eigenvalue, manifold, symmetric matrix","15A18","","","14:18:31","Tue Apr 01 2008","129.100.76.90"
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