(adsbygoogle = window.adsbygoogle || []).push({}); 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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# Stable matrices and their determinants

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