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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Note on nonnegative matrices


Author: D. Ž. Djoković
Journal: Proc. Amer. Math. Soc. 25 (1970), 80-82
MSC: Primary 15.60; Secondary 65.00
MathSciNet review: 0257114
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Abstract: Let $ A$ be a nonnegative square matrix and $ B = {D_1}A{D_2}$ where $ {D_1}$ and $ {D_2}$ are diagonal matrices with positive diagonal entries. Several proofs are known for the following theorem: If $ A$ is fully indecomposable then $ {D_1}$ and $ {D_2}$ can be chosen so that $ B$ is doubly stochastic. Moreover, $ {D_1}$ and $ {D_2}$ are unique up to a scalar factor. It is shown that these results can be easily obtained by considering a minimum of a certain rational function of several variables.


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DOI: http://dx.doi.org/10.1090/S0002-9939-1970-0257114-X
PII: S 0002-9939(1970)0257114-X
Keywords: Nonnegative matrix, doubly stochastic matrix, irreducible matrix, fully indecomposable matrix
Article copyright: © Copyright 1970 American Mathematical Society