Abstract
A scaling of a nonnegative matrixA is a matrixXAYź1, 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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