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Diagonal Elements of Doubly-Stochastic Matrices

Published online by Cambridge University Press:  03 November 2016

I. P. Gorton
I. P. Gorton*
Affiliation:
The University, Sheffield
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Extract

A square matrix is said to be doubly-stochastic if its elements are non-negative and if all row-sums and column-sums are equal to 1. The study of doubly-stochastic matrices was initiated by I. Schur and was subsequently taken up by Hardy, Littlewood, and Polya, who proved the following fundamental proposition [1, Theorem 46].

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Type
Research Article
Information
The Mathematical Gazette , Volume 45 , Issue 353 , October 1961, pp. 197 - 198
Copyright
Copyright © Mathematical Association 1961

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References

1. Hardy, G H., Little wood, J E., and Poly, G. a, Inequalities (Cambridge, 1934).Google Scholar
2. Horn, A., Doubly stochastic matrices and the diagonal of a rotation matrix, Amer. J Math. 76 (1954), 620–630.Google Scholar
3. Mirsky, L., An existence theorem for infinite matrices, Amer, Math. Monthly. 68 (1961), 465–469.CrossRefGoogle Scholar
4. Schur, I., Uber eine Klasse von Mittelbildungen mit Anwendung auf die Determinantentheorie, Sitzb. d. Berliner math. Ges. 22 (1923), 9–20.Google Scholar