Abstract
Let B be an n×n 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 n–s if and only if there exists an (n+k) ×(n+k) 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.
| Original language | American English |
|---|---|
| Pages (from-to) | 2313-2334 |
| Number of pages | 22 |
| Journal | Linear and Multilinear Algebra |
| Volume | 64 |
| Issue number | 11 |
| DOIs | |
| State | Published - Mar 7 2016 |
| Externally published | Yes |
Bibliographical note
Publisher Copyright:© 2016 Taylor & Francis.
ASJC Scopus Subject Areas
- Algebra and Number Theory
Keywords
- Birkhoff's theorem
- Doubly stochastic matrices
- Doubly substochastic matrices
- Permutation matrices
- doubly substochastic matrices
- Birkhoff’s theorem
- doubly stochastic matrices
- permutation matrices
Disciplines
- Mathematics
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