ELA, Volume 10, pp. 81-101, April 2003, abstract.

One-sided simultaneous inequalities and sandwich theorems for
diagonal similarity and diagonal equivalence of nonnegative
matrices

Daniel Hershkowitz and Hans Schneider

Results on the simultaneous scaling of nonnegative matrices 
involving one sided inequalities are presented. These are 
applied to scalings involving two sided inequalities. The 
proofs are graph theoretic. The setting is generalized to 
matrices with elements in lattice ordered Abelian groups 
with 0.