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stable matrix

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\begin{document}
A square matrix is said to be a \emph{stable matrix} if every eigenvalue
of has negative real part. The matrix is called \emph{positive
stable} if every eigenvalue has positive real part.

{\it Motivation:} In the following system of linear differential
equations,
\[
  \mathbf{x}'(t) = M \mathbf{x}(t)
\]
it is easy to see that the point $\mathbf{x}=\mathbf{0}$ is an
equilibrium point. The trajectory $\mathbf{x}(t)$ will converge to
$\mathbf{0}$ for every initial value $\mathbf{x}(0)$ if and only if
the matrix $M$ is a stable matrix.
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