Diagonal equivalence to matrices with prescribed row and column sums. II
Author:
Richard Sinkhorn
Journal:
Proc. Amer. Math. Soc. 45 (1974), 195198
MSC:
Primary 15A21
MathSciNet review:
0357434
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Abstract: Let be a nonnegative matrix and let and be positive vectors such that . It is well known that if there exists a nonnegative matrix with the same zero pattern as having the th row sum and th column sum , there exist diagonal matrices and with positive main diagonals such that has th row sum and th column sum . However the known proofs are at best cumbersome. It is shown here that this result can be obtained by considering the minimum of a certain realvalued function of positive variables.
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 R. A. Brualdi, Convex sets of nonnegative matrices, Canad. J. Math. 20 (1968), 144157. MR 36 #2636. MR 0219556 (36:2636)
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Additional Information
DOI:
http://dx.doi.org/10.1090/S00029939197403574348
PII:
S 00029939(1974)03574348
Keywords:
Nonnegative matrix,
diagonal equivalence,
fully indecomposable matrix,
zero pattern
Article copyright:
© Copyright 1974
American Mathematical Society
