Mathematics Faculty Proceedings, Presentations, Speeches, Lectures

Title

Sub-defect of Product of Doubly Substochastic Matrices

Event Name/Location

American Mathematical Society Spring Southeastern Sectional Meeting, Auburn, Alabama, March 15-17, 2019

Document Type

Conference Proceeding

Publication Date

3-15-2019

Abstract

The sub-defect of an n x n doubly substochastic matrix S, denoted by sd(S); is defined to be the smallest integer k such that there exists an (n + k) x (n + k) doubly stochastic matrix containing S as a submatrix. Let A and B be arbitrary doubly substochastic matrices. We show that AB is also a doubly substochastic matrix and max{sd(A), sd(B)} ≤ sd(AB) ≤ min{n, sd(A) + sd(B)}.

ORCID ID

0000-0001-7613-7191

ResearcherID

G-7341-2019

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