Mathematics Faculty Articles
Sub-Defect of Product of Doubly Substochastic Matrices
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)}.
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
Comments
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