I have to either prove or disprove with a counterexample the following staement:

"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 the eigen values of the m by m matrix AB are real."

Can anyone help? Please note that AB is not necessarily symmetric (Hermitian).

Is this a variant of the Perron–Frobenius theorem?

 

I do not know what row-stochastic matrix means.

I do not know what row-stochastic matrix means.

A matrix where the entries in each row are real, positive and add up to 1. In other words, each row represents a discrete probability distribution.

A matrix where the entries in each row are real, positive and add up to 1. In other words, each row represents a discrete probability distribution.

 

Cheers.

Cheers.

 

yeah, I didn't know that either... was thinking more along the lines of row-echelon.