Stochastic forms of non-negative matrices and Perron-regularity

Abstract

Given a real non-negative square matrix A, the problem of determining when two distinct constructions of stochastic matrices associated to A coincide is studied. All the constructions (or stochastic forms) that are considered are diagonal forms, i.e., the transformations act like A 􏰀→ αD^(r)AD^(c), where D^(r) and D^(c) are diagonal matrices with positive diagonals and α > 0, all depending on A.