A square matrix is said to be a stable matrix if every eigenvalue of has negative real part. The matrix is called positive stable if every eigenvalue has positive real part.

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.