The DAD theorem for arbitrary row sums-Reference-Cited by-同舟云学术

The DAD theorem for arbitrary row sums

Published:1974 Issue:2 Volume:45 Page:189-194
ISSN:0002-9939
Container-title:Proceedings of the American Mathematical Society
language:en
Short-container-title:Proc. Amer. Math. Soc.

Author:

Brualdi Richard A.

Abstract

Given an m × m m \times m symmetric nonnegative matrix A A and a positive vector R = ( r 1 , ⋯ , r m ) R = ({r_1}, \cdots ,{r_m}) , necessary and sufficient conditions are obtained in order that there exist a diagonal matrix D D with positive main diagonal such that DAD has row sum vector R R .

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics,General Mathematics

Link

http://www.ams.org/proc/1974-045-02/S0002-9939-1974-0354737-8/S0002-9939-1974-0354737-8.pdf

Reference11 articles.

1. The diagonal equivalence of a nonnegative matrix to a stochastic matrix;Brualdi, Richard A.;J. Math. Anal. Appl.,1966

2. Convex sets of non-negative matrices;Brualdi, R. A.;Canadian J. Math.,1968

3. \bysame, Combinatorial properties of symmetric nonnegative matrices, Proc. Internat. Conf. ’Combinatorial Theories’ held in Rome, Sept. 3-15, 1973 (to appear).

4. The 𝐷𝐴𝐷 theorem for symmetric non-negative matrices;Csima, J.;J. Combinatorial Theory Ser. A,1972

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