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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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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
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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Keywords: Nonnegative matrix, doubly stochastic matrix, irreducible matrix, fully indecomposable matrix
Article copyright: © Copyright 1970 American Mathematical Society