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.

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Mar 25th, 2:45 PM Mar 25th, 4:00 PM

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.