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The DAD theorem for arbitrary row sums


Author: Richard A. Brualdi
Journal: Proc. Amer. Math. Soc. 45 (1974), 189-194
MSC: Primary 15A48
DOI: https://doi.org/10.1090/S0002-9939-1974-0354737-8
MathSciNet review: 0354737
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Abstract: Given an $ m \times m$ symmetric nonnegative matrix $ A$ and a positive vector $ R = ({r_1}, \cdots ,{r_m})$, necessary and sufficient conditions are obtained in order that there exist a diagonal matrix $ D$ with positive main diagonal such that DAD has row sum vector $ R$.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1974-0354737-8
Keywords: Nonnegative matrix, diagonal matrix, symmetric matrix, completely reducible, completely decomposable, row sum vector
Article copyright: © Copyright 1974 American Mathematical Society

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