Diagonal equivalence to matrices with prescribed row and column sums. II

Author:
Richard Sinkhorn

Journal:
Proc. Amer. Math. Soc. **45** (1974), 195-198

MSC:
Primary 15A21

DOI:
https://doi.org/10.1090/S0002-9939-1974-0357434-8

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 real-valued function of positive variables.

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9939-1974-0357434-8

Keywords:
Nonnegative matrix,
diagonal equivalence,
fully indecomposable matrix,
zero pattern

Article copyright:
© Copyright 1974
American Mathematical Society