I need to either prove or disprove by a counterexample the following proposition:(adsbygoogle = window.adsbygoogle || []).push({});

" 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).

**Physics Forums | Science Articles, Homework Help, Discussion**

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Real eigen values

**Physics Forums | Science Articles, Homework Help, Discussion**