# What determines whether or not a matrix is stable?

1. Apr 19, 2007

### 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.

2. Apr 20, 2007

### 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?

3. Apr 20, 2007

### J77

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 $$\Delta=A-\lambda I$$.