Functional characterizations of the field of values and the convex hull of the spectrum
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- by Charles R. Johnson PDF
- Proc. Amer. Math. Soc. 61 (1976), 201-204 Request permission
Abstract:
The only compact, convex set-valued homogeneous and translatable function of square complex matrices which is an indicator function for the matrices with positive semidefinite real part is the classical field of values. An analogous characterization of the convex hull of the spectrum is given.References
- Charles R. Johnson, A Geršgorin inclusion set for the field of values of a finite matrix, Proc. Amer. Math. Soc. 41 (1973), 57–60. MR 318191, DOI 10.1090/S0002-9939-1973-0318191-3
- Charles R. Johnson, A Lyapunov theorem for angular cones, J. Res. Nat. Bur. Standards Sect. B 78B (1974), 7–10. MR 332836
- B. David Saunders and Hans Schneider, A symmetric numerical range for matrices, Numer. Math. 26 (1976), no. 1, 99–105. MR 447296, DOI 10.1007/BF01396569 C. Zenger, Minimum subadditive inclusion domains for the eigenvalues of matrices (to appear).
Additional Information
- © Copyright 1976 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 61 (1976), 201-204
- MSC: Primary 15A15; Secondary 47A10
- DOI: https://doi.org/10.1090/S0002-9939-1976-0437555-3
- MathSciNet review: 0437555