IJPAM: Volume 30, No. 4 (2006)
Department of Mathematics
Taipei, 11102, TAIWAN, R.O.C.
Department of Mathematical Sciences
Faculty of Science and Technology,
Hirosaki, 036-8561, JAPAN
Abstract.We deal with -by- matrices whose numerical ranges have elliptic boundary generating curves. The elliptic boundary generating curves are parametrized and classified for small . 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