# Rank relations between a {0, 1}-matrix and its complement

Rank relations between a {0, 1}-matrix and its complement AbstractLet A be a {0, 1}-matrix and r(A) denotes its rank. The complement matrix of A is defined and denoted by Ac = J − A, where J is the matrix with each entry being 1. In particular, when A is a square {0, 1}-matrix with each diagonal entry being 0, another kind of complement matrix of A is defined and denoted by A = J − I − A, where I is the identity matrix. We determine the possible values of r(A) ± r(Ac) and r(A) ± r(A) in the general case and in the symmetric case. Our proof is constructive. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Open Mathematics de Gruyter

# Rank relations between a {0, 1}-matrix and its complement

, Volume 16 (1): 6 – Mar 20, 2018
6 pages

Loading next page...

/lp/degruyter/rank-relations-between-a-0-1-matrix-and-its-complement-GBY07WDIoa
Publisher
de Gruyter
Copyright
© 2018 Ma and Zhong, published by De Gruyter
ISSN
2391-5455
eISSN
2391-5455
D.O.I.
10.1515/math-2018-0020
Publisher site
See Article on Publisher Site

### Abstract

AbstractLet A be a {0, 1}-matrix and r(A) denotes its rank. The complement matrix of A is defined and denoted by Ac = J − A, where J is the matrix with each entry being 1. In particular, when A is a square {0, 1}-matrix with each diagonal entry being 0, another kind of complement matrix of A is defined and denoted by A = J − I − A, where I is the identity matrix. We determine the possible values of r(A) ± r(Ac) and r(A) ± r(A) in the general case and in the symmetric case. Our proof is constructive.

### Journal

Open Mathematicsde Gruyter

Published: Mar 20, 2018

## You’re reading a free preview. Subscribe to read the entire article.

### DeepDyve is your personal research library

It’s your single place to instantly
discover and read the research
that matters to you.

Enjoy affordable access to
over 18 million articles from more than
15,000 peer-reviewed journals.

All for just $49/month ### Explore the DeepDyve Library ### Search Query the DeepDyve database, plus search all of PubMed and Google Scholar seamlessly ### Organize Save any article or search result from DeepDyve, PubMed, and Google Scholar... all in one place. ### Access Get unlimited, online access to over 18 million full-text articles from more than 15,000 scientific journals. ### Your journals are on DeepDyve Read from thousands of the leading scholarly journals from SpringerNature, Elsevier, Wiley-Blackwell, Oxford University Press and more. All the latest content is available, no embargo periods. DeepDyve ### Freelancer DeepDyve ### Pro Price FREE$49/month
\$360/year

Save searches from
Google Scholar,
PubMed

Create lists to
organize your research

Export lists, citations

Read DeepDyve articles

Abstract access only

Unlimited access to over
18 million full-text articles

Print

20 pages / month

PDF Discount

20% off