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?
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.