stable matrix

A square matrixMathworldPlanetmath is said to be a stable matrix if every eigenvalueMathworldPlanetmathPlanetmathPlanetmathPlanetmath 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,


it is easy to see that the point 𝐱=𝟎 is an equilibrium point. The trajectory 𝐱(t) will converge to 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