Abstract
Let B be an n x 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) x (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.
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Metadata
- Subject
Mathematics
- Institution
Gainesville
- Event location
Nesbitt 3218
- Event date
25 March 2016
- Date submitted
18 July 2022
- Additional information
Acknowledgements:
Dr. Selcuk Koyuncu