Abstract
A scaling of a nonnegative matrixA is a matrixXAY −1, whereX andY are nonsingular, nonnegative diagonal matrices. Some condition may be imposed on the scaling, for example, whenA is square,X=Y or detX=detY. We characterize matrices for which there exists a scaling that satisfies predetermined upper and lower bound. Our principal tools are a piecewise linear theorem of the alternative and a theorem decomposing a solution of a system of equations as a sum of minimal support solutions which conform with the given solutions.
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This research was partially supported by National Science Foundation Grants ENG-78-25182 and MCS-80-26132.
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v. Golitschek, M., Rothblum, U.G. & Schneider, H. A conforming decomposition theorem, a piecewise linear theorem of the alternative, and scalings of matrices satisfying lower and upper bounds. Mathematical Programming 27, 291–306 (1983). https://doi.org/10.1007/BF02591905
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DOI: https://doi.org/10.1007/BF02591905