A Note Concerning Simultaneous Integral Equations
1968 ◽
Vol 20
◽
pp. 855-861
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Keyword(s):
In (2) Sinkhorn showed that corresponding to each positive n × n matrix A (i.e., every aij > 0) is a unique doubly stochastic matrix of the form D1AD2, where each Dk is a diagonal matrix with a positive main diagonal. The Dk themselves are unique up to a scalar multiple. In (3) the result was extended to show that D1AD2 could be made to have arbitrarypositive row and column sums (with the reservation, of course, that the sum of the row sums equal the sum of the column sums) where A need no longer be square.
1966 ◽
Vol 18
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pp. 303-306
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1974 ◽
Vol 26
(3)
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pp. 600-607
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1959 ◽
Vol 26
(1)
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pp. 61-72
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1967 ◽
Vol 18
(2)
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pp. 244-244
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1959 ◽
Vol 11
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pp. 269-279
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Keyword(s):
2016 ◽
Vol 31
◽
pp. 593-609
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Keyword(s):
2017 ◽
Vol 532
◽
pp. 387-396
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