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,

$${𝐱}^{\prime }(t)=M𝐱(t)$$

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

Title	stable matrix
Canonical name	StableMatrix
Date of creation	2013-03-22 15:27:40
Last modified on	2013-03-22 15:27:40
Owner	rspuzio (6075)
Last modified by	rspuzio (6075)
Numerical id	8
Author	rspuzio (6075)
Entry type	Definition
Classification	msc 34D23
Classification	msc 15A57
Defines	positive stable