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′(t)=M𝐱(t) |
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 |