# 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 $\mathbf{x}=\mathrm{\U0001d7ce}$ is an equilibrium point. The trajectory $\mathbf{x}(t)$ will converge to $\mathrm{\U0001d7ce}$ for every initial value $\mathbf{x}(0)$ 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 |