IJPAM: Volume 30, No. 4 (2006)


Mao-Ting Chien$^1$, Hiroshi Nakazato$^2$
$^1$Department of Mathematics
Soochow University
Taipei, 11102, TAIWAN, R.O.C.
e-mail: mtchien@scu.edu.tw
$^2$Department of Mathematical Sciences
Faculty of Science and Technology,
Hirosaki University
Hirosaki, 036-8561, JAPAN
e-mail: nakahr@cc.hirosaki-u.ac.jp

Abstract.We deal with $n$-by-$n$ matrices whose numerical ranges have elliptic boundary generating curves. The elliptic boundary generating curves are parametrized and classified for small $n$. Examples are constructed for each class. From a graph theoretical view point, we give a blockwise nilpotent Toeplitz matrix whose boundary generating curve has genus 1, the curve is elliptic but not rational.

Received: June 6, 2006

AMS Subject Classification: 15A60, 14H52

Key Words and Phrases: numerical ranges, elliptic curves, boundary generating curves, genus

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2006
Volume: 30
Issue: 4