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Real eigen values

  1. Jan 27, 2012 #1
    I need to either prove or disprove by a counterexample the following proposition:
    " Let A be an m by n row-stochastic matrix in which all entries are positive real numbers and let B be an n by m column-stochastic matrix with the same feature. Then all eigen values of the m by m matrix AB are real."
    Can anyone help? It may be noted that AB is not necessarily symmetric (Hermitian).
    Last edited: Jan 28, 2012
  2. jcsd
  3. Jan 27, 2012 #2


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    Hello asisbanerjee and welcome to the forums.

    Maybe this will give you a headstart:

  4. Jan 28, 2012 #3


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    Do you know an example of a (square) stochastic matrix A whose entries are positive but which has a nonreal eigenvalue?

    That's enough to find a counterexample, because you can then take B=...
    Last edited: Jan 28, 2012
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