Geodesic
Applications of max algebra to diagonal scaling of matrices
The electronic journal of linear algebra, Tome 13 (2005), pp. 262-273.

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Summary: 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.
Classification : 15A24, 15A15, 15A48, 90C27
Keywords: Max algebra inequality, diagonal scaling, term rank scaling, algorithm 
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     author = {Butkovic, Peter and Schneider, Hans},
     title = {Applications of max algebra to diagonal scaling of matrices},
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Butkovic, Peter; Schneider, Hans. Applications of max algebra to diagonal scaling of matrices. The electronic journal of linear algebra, Tome 13 (2005), pp. 262-273. http://geodesic.mathdoc.fr/item/ELA_2005__13__a6/