  In this paper, we describe the general framework to describe the diffusion
operators associated to a positive matrix. We define the equations associated
to diffusion operators and present some general properties of their state
vectors. We show how this can be applied to prove and improve the convergence
of a fixed point problem associated to the matrix iteration scheme. The
approach can be understood as a decomposition of the matrix-vector product
operation in elementary operation at the vector entry level.
