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Normality and the Higher Numerical Range

Published online by Cambridge University Press:  20 November 2018

Marvin Marcus ,
Benjamin N. Moyls  and
Ivan Filippenko
Marvin Marcus
Affiliation:
University of California, Santa Barbara, California
Benjamin N. Moyls
Affiliation:
University of California, Santa Barbara, California
Ivan Filippenko
Affiliation:
University of California, Santa Barbara, California
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Let Mn(C) be the vector space of all w-square complex matrices. Denote by (• , •) the standard inner product in the space Cn of complex n-tuples. For a matrix A ∈ Mn(C) and an n-tuple c = (c1,… , cn) ∈ Cn, define the c-numerical range of A to be the set

(1)

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 30 , Issue 2 , 01 April 1978 , pp. 419 - 430
Copyright
Copyright © Canadian Mathematical Society 1978

References

1. Fillmore, P. A. and Williams, J. P., Some convexity theorems for matrices, Glasgow Math. J. 12 (1971), 110–117.Google Scholar
2. Halmos, P. R., A Hilbert space problem book (Van Nostrand Co., Inc., 1967).Google Scholar
3. Horn, A., Doubly stochastic matrices and the diagonal of a rotation matrix, Amer. J. Math. 76 (1954), 620–630.Google Scholar
4. Marcus, M. and Minc, H., A survey of matrix theory and matrix inequalities (Prindle, Weber and Schmidt, Inc., Boston, 1964).Google Scholar
5. Marcus, M., Moyls, B.N., and Westwick, R., Some extreme value results for indefinite hermitian matrices, II, Illinois J. Math. 2 (1958), 408–414.Google Scholar
6. Moyls, B. N. and Marcus, M., Field convexity of a square matrix, Proc. Amer. Math. Soc. G (1955), 981–983.Google Scholar
7. Murnaghan, F. D., On the field of values of a square matrix, Proc. Nat. Acad. Sci. 18 (1932), 246–248.Google Scholar