Diagonals of Nonnegative Matrices

Paul Erdös, Henryk Minc, Paul Erdös, Henryk Minc

Research output: Contribution to journalArticle

4 Citations (Scopus)

Abstract

Let (a1, …, an), (r1, …, rn) and (c1, …, cn) be real n-tuples, n ⩾ 3, satisfying [formula omitted] It is shown that a necessary and sufficient condition for the existence of a non-negative matrix with main diagonal (a1, …, an), with row sums r1,…, rn and column sums c1, …, cn, is that [formula omitted] Equality can hold if and only if all the off-diagonal positive entries of the matrix are restricted to the kth row and the kth column, for some k, 1 ⩽ k ⩽ n.

Original languageEnglish
Pages (from-to)89-95
Number of pages7
JournalLinear and Multilinear Algebra
Volume1
Issue number2
DOIs
Publication statusPublished - Jan 1 1973

ASJC Scopus subject areas

  • Algebra and Number Theory

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