Some Results on the q-Numerical
Chi-Kwong Li, Hiroshi Nakazato · Linear and Multilinear Algebra · 1998
Let q be a complex number with . The q-numerical range of an n × n complex matrix A is defined by . In the last few years, the q-numerical range has attracted the attention of a number of authors, and many interesting results have been obtained. In this paper, we further the study of this subject. In particular, we prove a theorem relating the q-numerical range and the Davis-Wielandt shell. We also study some scalar functions associated with the q numerical range, and get some partial result for a question raised in a recent paper by Aleksiejczyk. Some algorithms for generating the q-numerical range and the Davis Wielandt shell are given.