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Stable matrices and their determinants

by Tonyt88
Tags: determinants, matrices, stable
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Apr13-07, 01:36 AM
P: 62
1. The problem statement, all variables and given/known data
Consider a dynamical system x(t+1) = Ax(t),, where A is a real n x n matrix.
(a) If |det(A)| > or equal to one, what can you say about the stability of the zero state?
(b) If |det(A)| < 1, what can you say about the stability of the zero state?

2. Relevant equations

3. The attempt at a solution
I have worked with various matrices knowing if they are stable or not and the value of the determinants, but from what I can see, there exists no relation between the determinant and the stability of the matrix, so basically, where to go from here?
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Apr13-07, 02:35 AM
P: 1,235
I am used to look at such questions by taking the eigenvectors as basis.
Then everything is understood on the basis of simple numbers: the eigenvalues.

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