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Homestable matrix

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# 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.

Defines:

positive stable

Type of Math Object:

Definition

Major Section:

Reference

## Mathematics Subject Classification

34D23*no label found*15A57

*no label found*

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