Article
Sub-Defect of Product of Doubly Substochastic Matrices
Linear and Multilinear Algebra
Document Type
Article
Publication Date
4-1-2017
Keywords
- Doubly stochastic matrices,
- Doubly substochastic matrices,
- Sub-defect
Disciplines
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
ORCID ID
0000-0001-7613-7191
ResearcherID
G-7341-2019
DOI
10.1080/03081087.2018.1513448
Citation Information
Lei Cao and Selcuk Koyuncu. "Sub-Defect of Product of Doubly Substochastic Matrices" Linear and Multilinear Algebra Vol. 65 Iss. 4 (2017) p. 653 - 657 ISSN: 0308-1087 Available at: http://works.bepress.com/lei-cao/20/
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