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Note on nonnegative matrices


Author: D. Ž. Djoković
Journal: Proc. Amer. Math. Soc. 25 (1970), 80-82
MSC: Primary 15.60; Secondary 65.00
DOI: https://doi.org/10.1090/S0002-9939-1970-0257114-X
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.


References [Enhancements On Off] (What's this?)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1970-0257114-X
Keywords: Nonnegative matrix, doubly stochastic matrix, irreducible matrix, fully indecomposable matrix
Article copyright: © Copyright 1970 American Mathematical Society

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