Sub-Defect of Product of Doubly Substochastic Matrices

Authors

Lei Cao, Georgian Court UniversityFollow
Selcuk Koyuncu, University of North Georgia

Document Type

Article

Publication Date

4-2017

Publication Title

Linear and Multilinear Algebra

Keywords

Doubly stochastic matrices, Doubly substochastic matrices, Sub-defect

ISSN

0308-1087

Volume

65

Issue/No.

4

First Page

653

Last Page

657

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)}.

Comments

©2018 Informa UK Limited, trading as Taylor & Francis Group

Additional Comments

National Natural Science Foundation of China grant #s: 11601233; Fundamental Research Funds for the Central Universities grant #: KYZ201650; Natural Science Foundation of Jiangsu Province grant #: BK20160708

NSUWorks Citation

Cao, Lei and Koyuncu, Selcuk, "Sub-Defect of Product of Doubly Substochastic Matrices" (2017). Mathematics Faculty Articles. 271.
https://nsuworks.nova.edu/math_facarticles/271

ORCID ID

0000-0001-7613-7191

ResearcherID

G-7341-2019

DOI

10.1080/03081087.2018.1513448