Accession Number : AD0657579

Title :   MATRIX LINKS, AN EXTREMIZATION PROBLEM, AND THE REDUCTION OF A NON-NEGATIVE MATRIX TO ONE WITH PRESCRIBED ROW AND COLUMN SUMS.

Descriptive Note : Technical summary rept.,

Corporate Author : WISCONSIN UNIV MADISON MATHEMATICS RESEARCH CENTER

Personal Author(s) : Menon,M. V.

Report Date : JUN 1967

Pagination or Media Count : 19

Abstract : 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, j>1, certain matrix operations are defined which when applied to each A a member of alpha lead to two matrices whose first row sums equal Sup(subscript A a member of alpha) (first row sum of A) and Inf(subscript 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.

Descriptors :   (*MATRICES(MATHEMATICS), THEOREMS), ALGORITHMS, LINEAR PROGRAMMING, MATHEMATICS

Subject Categories : Theoretical Mathematics

Distribution Statement : APPROVED FOR PUBLIC RELEASE