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Nonsquare "Doubly Stochastic" Matrices

R. M. Caron, Xin Li, P. Mikusiński, H. Sherwood and M. D. Taylor
Lecture Notes-Monograph Series
Vol. 28, Distributions with Fixed Marginals and Related Topics (1996), pp. 65-75
Stable URL: http://www.jstor.org/stable/4355884
Page Count: 11
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Nonsquare
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Abstract

An n × m non-negative matrix with uniform row sum m and column sum n is called a "doubly stochastic" matrix. When n = m, such a matrix is a scale multiple of a doubly stochastic matrix in its classical sense. Garrett Birkhoff proved a theorem characterizing all classical extremal doubly stochastic matrices as permutation matrices. We will discuss the characterization of the extremal matrices for nonsquare "doubly stochastic" matrices in the spirit of Birkhoff's theorem.

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