Vol. 2, No. 8, 2008

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

Volume 10
Issue 9, 1845–2052
Issue 8, 1601–1843
Issue 7, 1373–1600
Issue 6, 1147–1371
Issue 5, 939–1146
Issue 4, 695–938
Issue 3, 451–694
Issue 2, 215–450
Issue 1, 1–214

Volume 9, 10 issues

Volume 8, 10 issues

Volume 7, 10 issues

Volume 6, 8 issues

Volume 5, 8 issues

Volume 4, 8 issues

Volume 3, 8 issues

Volume 2, 8 issues

Volume 1, 4 issues

The Journal
Cover
Editorial Board
Editors' Addresses
Editors' Interests
About the Journal
Scientific Advantages
Submission Guidelines
Submission Form
Subscriptions
Editorial Login
Contacts
Author Index
To Appear
 
ISSN: 1944-7833 (e-only)
ISSN: 1937-0652 (print)
The number of 2$\times$2 integer matrices having a prescribed integer eigenvalue

Greg Martin and Erick Wong

Vol. 2 (2008), No. 8, 979–1000
Abstract

What is the probability that an integer matrix chosen at random has a particular integer as an eigenvalue, or an integer eigenvalue at all? For a random real matrix, what is the probability of there being a real eigenvalue in a particular interval? This paper solves these questions for 2 × 2 matrices, after specifying the probability distribution suitably.

Keywords
random matrix, eigenvalue, integer eigenvalue, integer matrix, distribution of eigenvalues
Mathematical Subject Classification 2000
Primary: 15A36, 15A52
Secondary: 11C20, 15A18, 60C05
Milestones
Received: 28 May 2008
Revised: 13 August 2008
Accepted: 16 October 2008
Published: 23 November 2008
Authors
Greg Martin
Department of Mathematics
University of British Columbia
Room 121, 1984 Mathematics Road
Vancouver, BC V6T 1Z2
Canada
http://www.math.ubc.ca/~gerg
Erick Wong
Department of Mathematics
University of British Columbia
Room 121, 1984 Mathematics Road
Vancouver, BC V6T 1Z2
Canada
http://www.math.ubc.ca/~erick