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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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A simple proof of the elliptical range theorem
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by Chi-Kwong Li PDF
Proc. Amer. Math. Soc. 124 (1996), 1985-1986 Request permission

Abstract:

A short proof is given of the elliptical range theorem concerning the numerical range of a $2\times 2$ complex matrix.
References
  • T. Ando and C.K. Li (Editors), Special Issue: The Numerical Range and Numerical Radius, Linear and Multilinear Algebra 37, nos. 1 – 3, 1994.
  • William F. Donoghue Jr., On the numerical range of a bounded operator, Michigan Math. J. 4 (1957), 261–263. MR 96127
  • Paul R. Halmos, A Hilbert space problem book, D. Van Nostrand Co., Inc., Princeton, N.J.-Toronto, Ont.-London, 1967. MR 0208368
  • Roger A. Horn and Charles R. Johnson, Topics in matrix analysis, Cambridge University Press, Cambridge, 1994. Corrected reprint of the 1991 original. MR 1288752
  • Vasile I. Istrăţescu, Introduction to linear operator theory, Monographs and Textbooks in Pure and Applied Mathematics, vol. 65, Marcel Dekker, Inc., New York, 1981. MR 608969
  • F.D. Murnaghan, On the field of values of a square matrix, Proc. Natl. Acad. Sci. 18 (1932), 246-248.
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Additional Information
  • Chi-Kwong Li
  • Affiliation: Department of Mathematics, College of William and Mary, Williamsburg, Virginia 23187
  • MR Author ID: 214513
  • Email: ckli@cs.wm.edu
  • Received by editor(s): January 17, 1995
  • Additional Notes: This research was supported in part by a NATO grant.
  • Communicated by: Palle E. T. Jorgensen
  • © Copyright 1996 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 124 (1996), 1985-1986
  • MSC (1991): Primary 15A60
  • DOI: https://doi.org/10.1090/S0002-9939-96-03307-2
  • MathSciNet review: 1322932