Faculty Mentor(s)
Dr. Selcuk Koyuncu
Campus
Gainesville
Proposal Type
Presentation - completed/ongoing
Subject Area
Mathematics
Location
Nesbitt 3218
Start Date
25-3-2016 2:45 PM
End Date
25-3-2016 4:00 PM
Description/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.
Rights
This has been published by "The Journal of Linear and Multilinear Algebra", I am a co-author with Dr. Selcuk Koyuncu of the University of North Georgia and Dr. Lei Cao of Drexel University.
A minimal completion of double substochastic matrices
Nesbitt 3218
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.