ICM 1998, Berlin, Aug. 18–27

Abstracts of Short Communications and Posters

Section:

8. Analysis

1991 MS Classification: 15, 47 Chien, Mao-Ting, Soochow University, Taiwan A parametrization of the c-numerical ranges of certain matrices Let A ∈ M_{n}, the n-by-n complex matrices. For an n-tuple c = (c_{1}, c_{2}, ⋯, c_{n}) in R^{n}, the c-numerical range of A is the set W_{c}(A) = {∑_{j=1}^{n}c_{j}x_{j}^{∗}Ax_{j} : {x_{1}, x_{2}, ⋯, x_{n}} is an orthonormal basis of C^{n}}. We give a parametrization of the c-numerical ranges of idempotent matrices, and give a necessary and sufficient condition for the c-numerical range of an idempotent matrix to be an elliptical disc. Reference M. T. Chien, The envelope of the generalized numerical range, Lin. Multilin. Alg. 43(1998), 363-376.