# stable matrix

## Primary tabs

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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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