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

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.

Document Details

Document Type
Technical Report
Publication Date
Jun 01, 1967
Accession Number
AD0657579

Entities

People

  • M. V. Menon

Organizations

  • University of Wisconsin–Madison

Tags

Communities of Interest

  • Air Platforms

Fields of Study

  • Mathematics

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