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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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Nonnegative matrices each of whose positive diagonals has the same sum
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by Mark Blondeau Hedrick PDF
Proc. Amer. Math. Soc. 59 (1976), 399-403 Request permission

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.
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Additional Information
  • © Copyright 1976 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 59 (1976), 399-403
  • MSC: Primary 15A48
  • DOI: https://doi.org/10.1090/S0002-9939-1976-0414595-1
  • MathSciNet review: 0414595