ELA, Volume 13, pp. 262-273, November 2005, abstract.

Applications of Max Algebra to Diagonal Scaling of Matrices

Peter Butkovic and Hans Schneider

Results are proven on an inequality in max algebra 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 
matrix to a matrix with 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.