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Stable matrices and their determinants 
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#1
Apr1307, 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? 


#2
Apr1307, 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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