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A note on multivariate majorization. (English) Zbl 1513.15036

Summary: A matrix \(A\) is said to be multivariate majorized by a matrix \(B\), written \(A\prec B\), if there exists a doubly stochastic matrix \(D\) such that \(A = BD\). In the present paper, we obtain a totally ordered subset of \(M_{nm}\) which contains a given matrix \(A\). Also, we show that the totality of all extreme points of the collection of all the matrices which are multivariately majorized by a matrix \(A\) is the set of all matrices obtained by permuting the columns of \(A\).

MSC:

15A45 Miscellaneous inequalities involving matrices
15B51 Stochastic matrices
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