The theory of numerical range in finite-dimensional spaces is very rich and varied. In fact, a lot of recent research has been focused on the numerical range, and its variations, in finite dimensions. Avoiding the evidently impossible task of doing justice to all of the work done in this field, we attempt to present a representative selection and hope that it covers all the basic material.
KeywordsConvex Hull Matrix Norm Maximum Eigenvalue Finite Dimension Numerical Range
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Notes and References
Notes and References for Section 5.1
Notes and References for Section 5.2
- S. Gersgorin (1931). “über die Abrenzung der Eigenwerte einer Matrix,” Izv. Akad. Nauk SSSR (Ser. Mat.) 7, 749–754.Google Scholar
- V. N. Solov’ev (1983). “A Generalization of Gersgorin’s Theorem,” Izv. Akad. Nauk. SSSR Ser. Mat. 47, 1285–1302; English translation in Math. USSR Izv. 23 (1984)Google Scholar
Notes and References for Section 5.3
Notes and References for Section 5.4
Notes and References for Section 5.5
- N. K. Tsing and W. S. Cheung (1996). “Star-Shapedness of the Generalized Numerical Ranges,” in Abstracts 3rd Workshop on Numerical Ranges and Numerical Radii ( T. Ando and K. Okubo, eds.), Sapporo, Japan.Google Scholar
Notes and References for Section 5.6
- L. N. Trefethen (1990). “Approximation Theory and Numerical Linear Algebra,” in Algorithms for Approximation. II, eds. J. Mason and M. Cox, Chapman, London, 336–360.Google Scholar