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A simple proof of the elliptical range theorem

Author(s): Chi-Kwong Li
Journal: Proc. Amer. Math. Soc. 124 (1996), 1985-1986.
MSC (1991): Primary 15A60
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Abstract: A short proof is given of the elliptical range theorem concerning the numerical range of a $2\times 2$ complex matrix.

References:

[AL]: T. Ando and C.K. Li (Editors), Special Issue: The Numerical Range and Numerical Radius, Linear and Multilinear Algebra 37, nos. 1 -- 3, 1994. CMP 95:07
[D]: W.F. Donoghue, On the numerical range of a bounded operator, Michigan J. Math. 4 (1957), 261-263. MR 20:2622
[H]: P.R. Halmos, A Hilbert Space Problem Book, Van Nostrand, New York, 1967. MR 34:8178
[HJ]: R.A. Horn and C.R. Johnson, Topics in Matrix Analysis, Cambridge University Press, 1991. MR 95c:15001
[I]: V. Istratescu, Introduction to Linear Operator Theory, Marcel Dekker, New York, 1981. MR 83d:47002
[M]: F.D. Murnaghan, On the field of values of a square matrix,


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