# stable matrix

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,

 $\mathbf{x}^{\prime}(t)=M\mathbf{x}(t)$

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.

Title stable matrix StableMatrix 2013-03-22 15:27:40 2013-03-22 15:27:40 rspuzio (6075) rspuzio (6075) 8 rspuzio (6075) Definition msc 34D23 msc 15A57 positive stable