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%"Vander Meulen","Kevin","kvanderm@cs.redeemer.ca","


\section*{Sparse Inertially Arbitrary Sign Patterns} By {\sl L. Vanderspek, M. Cavers, K.N. Vander Meulen$^*$}.  

\bigskip \noindent The inertia of a real matrix $A$ is an ordered triple $i(A)=(n_1,n_2,n_3)$ where $n_1$ is the number of eigenvalues of $A$ with positive real part, $n_2$ is the number of eigenvalues of $A$ with negative real part, and $n_3$ is the number of eigenvalues of $A$ with zero real part. A sign pattern is a matrix whose entries are in $\{ +,-,0\}$.  An order $n$ sign pattern $S$ is inertially arbitrary if for every ordered triple $(n_1,n_2,n_3)$ with $n_1+n_2+n_3=n$ there is a real matrix $A$ such that $A$ has sign pattern $S$ and $i(A)=(n_1,n_2,n_3)$. We describe some techniques in determining a pattern is inertially arbitrary. We present some irreducible inertially arbitrary patterns of order $n$ with less than $2n$ entries.
%","sign pattern, inertia, nilpotent","15A18","05C50","MS1 Combinatorial Matrix Theory","15:58:12","Tue Apr 01 2008","72.38.23.115"
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