Stable matrices and their determinants

  1. 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. jcsd
  3. 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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