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Limit of two matrices each to the kth power and multiplied

  1. Jul 4, 2013 #1
    If I have two square nonnegative primitive matrices where the Perron-Frobenius Theorem applies how would I calculate lim (A^k)(B^k) as k approaches infinity.
  2. jcsd
  3. Jul 4, 2013 #2
    I'm assuming I would just find A^k and B^k by diagonalization multiply them and then find the limit?
  4. Jul 4, 2013 #3

    Simon Bridge

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    You would probably be expected to exploit the properties of those non-negative primitive matrices which P-F can be applied to. I'd start by working though the definitions - bearing in mind what you understand about matrix manipulations. Note: there is a fair amount of overlap between the three conditions:

    is it possible to have a primitive matrix that is not non-negative?
    what sorts of matrices can F-P be applied to?
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