stable matrix

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

Motivation: In the following system of linear differentialequations,

$${𝐱}^{\prime }(t)=M𝐱(t)$$

it is easy to see that the point $𝐱=\mathrm{𝟎}$ is anequilibrium point. The trajectory $𝐱(t)$ will converge to$\mathrm{𝟎}$ for every initial value $𝐱(0)$ if and only ifthe matrix $M$ is a stable matrix.