## Mathematics Faculty Proceedings, Presentations, Speeches, Lectures

# Sub-defect of Product of Doubly Substochastic Matrices

## Event Name/Location

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

## Presentation Date

3-15-2019

## Document Type

Conference Proceeding

## ORCID ID

0000-0001-7613-7191

## ResearcherID

G-7341-2019

## Description

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*)}.

## NSUWorks Citation

Koyuncu, Selcuk and Cao, Lei, "Sub-defect of Product of Doubly Substochastic Matrices" (2019). *Mathematics Faculty Proceedings, Presentations, Speeches, Lectures*. 403.

https://nsuworks.nova.edu/cnso_math_facpres/403

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