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Geometry of the numerical range of matrices. (English) Zbl 0452.15024


MSC:

15A60 Norms of matrices, numerical range, applications of functional analysis to matrix theory
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References:

[1] Ballantine, C. S., Numerical range of a matrix: some effective criteria, Linear Algebra and Appl., 19, 117-188 (1978) · Zbl 0381.15010
[2] Donoghue, W. F., On the numerical range of a bounded operator, Michigan Math. J., 4, 261-263 (1957) · Zbl 0082.11601
[3] Fiedler, M., Additive compound matrices and an inequality for eigenvalues of symmetric stochastic matrices, Czechoslovak Math. J., 24, 392-402 (1974) · Zbl 0345.15013
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[5] Issos, J. N., The field of values of non-negative irreducible matrices, (Ph.D. Thesis (1966), Auburn Univ.)
[6] Kato, T., Perturbation Theory for Linear Operators (1979), Springer: Springer Berlin
[7] Kippenhahn, R., Über den Wetevorrat einer Matrix, Math. Nachr., 6, 193-228 (1951) · Zbl 0044.16201
[8] Levinger, B. W., An inequality for nonnegative matrices, Notices Amer. Math. Soc., 17, 260 (1970)
[9] Murnaghan, F. O., On the field of values of a square matrix, Proc. Nat. Acad. Sci. U.S.A., 18, 246-248 (1932) · Zbl 0004.05003
[10] Parker, W. V., Characteristic roots and field of values of a matrix, Bull. Amer. Math. Soc., 57, 103-108 (1951) · Zbl 0042.25101
[11] Rao, C. R.; Mitra, S. K., Generalized Inverse of Matrices and Its Applications (1971), Wiley: Wiley New York · Zbl 0236.15004
[12] Walker, R. J., Algebraic Curves (1950), Princeton U.P.,: Princeton U.P., Princeton, N.J. · Zbl 0039.37701
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