A minimal completion of doubly substochastic matrix

Let B be an doubly substochastic matrix and let s be the sum of all entries of B. In this paper, we show that B has a sub-defect of k,  which can be computed by taking the ceiling of if and only if there exists an doubly stochastic extension containing B as a submatrix and k minimal. We also propose...

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Published inLinear & multilinear algebra Vol. 64; no. 11; pp. 2313 - 2334
Main Authors Cao, Lei, Koyuncu, Selcuk, Parmer, Timmothy
Format Journal Article
LanguageEnglish
Published Abingdon Taylor & Francis 01.11.2016
Taylor & Francis Ltd
Subjects
Algebra
Birkhoff's theorem
Ceilings
Combinations (mathematics)
Computation
doubly stochastic matrices
doubly substochastic matrices
permutation matrices
Permutations
Stochasticity
Online AccessGet full text
ISSN0308-1087
1563-5139
DOI10.1080/03081087.2016.1155531

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Summary:Let B be an doubly substochastic matrix and let s be the sum of all entries of B. In this paper, we show that B has a sub-defect of k,  which can be computed by taking the ceiling of if and only if there exists an doubly stochastic extension containing B as a submatrix and k minimal. We also propose a procedure constructing a minimal completion of B, and then express it as a convex combination of partial permutation matrices.
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ISSN:0308-1087
1563-5139
DOI:10.1080/03081087.2016.1155531