Applications of max algebra to diagonal scaling of matrices

Abstract

Results are proven on an inequality in maxalgebra and applied to theorems on the
diagonal similarity scaling of matrices. Thus the set of all solutions to several scaling problems is
obtained. Also introduced is the “full term rank” scaling of a matrixto a matrixwith prescribed
row and column maxima with the additional requirement that all the maxima are attained at entries
each from a different row and column. An algorithm which finds such a scaling when it exists is
given.