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Proceedings of the American Mathematical Society

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Nonnegative matrices each of whose positive diagonals has the same sum

Author: Mark Blondeau Hedrick
Journal: Proc. Amer. Math. Soc. 59 (1976), 399-403
MSC: Primary 15A48
MathSciNet review: 0414595
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Abstract: The author shows that if $ A$ is a fully indecomposable nonnegative matrix each of whose positive diagonals has sum $ M$ and when $ {a_{ij}} = 0$, the sum of each positive diagonal in the submatrix of $ A$ obtained by deleting the $ i{\text{th}}$ row and $ j{\text{th}}$ column is less than $ M$, then there is a unique positive matrix $ B$ such that its rank is at most two, each of its diagonals has sum $ M$, and $ {a_{ij}} = {b_{ij}}$ when $ {a_{ij}} > 0$. The author then compares his results to those obtained by Sinkhorn and Knopp who carried out a similar analysis for positive diagonal products.

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

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Keywords: Fully indecomposable, doubly stochastic pattern, elementary symmetric function of a diagonal
Article copyright: © Copyright 1976 American Mathematical Society

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