What determines whether or not a matrix is stable?

[Tonyt88]

Basically, I'm having difficulty understanding the concept of stability, I have reread the chapter in my book various times, but to no avail. Can anybody give a very brief overview in simplified terms as to what determines whether or not a matrix is stable. Thanks.

 

[matt grime]

You're posting this in the algebra section. So do you mean things like stability conditions of representations of quivers? I doubt it. What topic do you really mean?

 

[J77]

Judging from your earlier post: https://www.physicsforums.com/showthread.php?p=1301361#post1301361 ...

you want to find the stability in terms of the eigenvalues $$\lambda$$ of an $$n\times n$$ matrix $$A$$.

In which case, you first step is to compute the determinant of $$\Delta$$; the characteristic equation given by $$\Delta=A-\lambda I$$.