MATRIX LINKS, AN EXTREMIZATION PROBLEM, AND THE REDUCTION OF A NON-NEGATIVE MATRIX TO ONE WITH PRESCRIBED ROW AND COLUMN SUMS.
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WISCONSIN UNIV MADISON MATHEMATICS RESEARCH CENTER
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If alpha is the class of non-negative m x n matrices A of a given pattern, with a11 0 and with prescribed i th row sum and j th column sum, i, j1, certain matrix operations are defined which when applied to each A a member of alpha lead to two matrices whose first row sums equal Supsubscript A a member of alpha first row sum of A and Infsubscript A a member of alpha first row sum of A. This result is used in the proof of the following one. Let A be a given non-negative matrix. Let alpha be the class of non-negative matrices of the same pattern as A and with all its row and column sums prescribed. If alpha is not empty, there exists a unique A a member of alpha and two diagonal matrices U and V such that A UAV.
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