Vol. 9, No. 2, 2016

Download this article
Download this article For screen
For printing
Recent Issues

Volume 13
Issue 3, 361–539
Issue 2, 181–360
Issue 1, 1–180

Volume 12, 8 issues

Volume 11, 5 issues

Volume 10, 5 issues

Volume 9, 5 issues

Volume 8, 5 issues

Volume 7, 6 issues

Volume 6, 4 issues

Volume 5, 4 issues

Volume 4, 4 issues

Volume 3, 4 issues

Volume 2, 5 issues

Volume 1, 2 issues

The Journal
About the Journal
Editorial Board
Editors’ Interests
Submission Guidelines
Submission Form
Policies for Authors
Ethics Statement
ISSN: 1944-4184 (e-only)
ISSN: 1944-4176 (print)
Author Index
Coming Soon
Other MSP Journals
This article is available for purchase or by subscription. See below.
The kernel of the matrix $\lbrack i\mskip-2mu j \pmod n\rbrack$ when $n$ is prime

Maria I. Bueno, Susana Furtado, Jennifer Karkoska, Kyanne Mayfield, Robert Samalis and Adam Telatovich

Vol. 9 (2016), No. 2, 265–280

In this paper, we consider the n × n matrix whose (i,j)-th entry is ij(modn) and compute its rank and a basis for its kernel (viewed as a matrix over the real numbers) when n is prime. We also give a conjecture on the rank of this matrix when n is not prime and give a set of vectors in its kernel, which is a basis if the conjecture is true. Finally, we include an application of this problem to number theory.

PDF Access Denied

However, your active subscription may be available on Project Euclid at

We have not been able to recognize your IP address as that of a subscriber to this journal.
Online access to the content of recent issues is by subscription, or purchase of single articles.

Please contact your institution's librarian suggesting a subscription, for example by using our journal-recom­mendation form. Or, visit our subscription page for instructions on purchasing a subscription.

You may also contact us at contact@msp.org
or by using our contact form.

Or, you may purchase this single article for USD 30.00:

rank of a matrix, kernel of a matrix, bisymmetric matrix.
Mathematical Subject Classification 2010
Primary: 15A03, 11M06, 11M20
Received: 14 October 2014
Revised: 13 April 2015
Accepted: 16 April 2015
Published: 2 March 2016

Communicated by Kenneth S. Berenhaut
Maria I. Bueno
Mathematics Department and College of Creative Studies
The University of California, Santa Barbara
Santa Barbara, CA 93106-3080
United States
Susana Furtado
Faculdade de Economia
Universidade do Porto
4200-464 Porto
Jennifer Karkoska
Applied Mathematics Department
Rensselaer Polytechnic Institute
Troy, NY 12180
United States
Kyanne Mayfield
Fast Enterprises LLC
Madison, WI 53704
United States
Robert Samalis
Department of Mathematics
University of Georgia
Athens, GA 30602
United States
Adam Telatovich
Department of Mathematics
Pennsylvania State University
State College, PA 16803
United States