On some 4-by-4 matrices with bi-elliptical numerical ranges

Linear and Multilinear Algebra, vol. 69, pp. 855–870

Abstract

A complete description of 4-by-4 matrices αICDβI, with scalar 2-by-2 diagonal blocks, for which the numerical range is the convex hull of two non-concentric ellipses is given. This result is obtained by reduction to the leading special case in which C−D∗ also is a scalar multiple of the identity. In particular cases when in addition α−β is real or pure imaginary, the results take an especially simple form. An application to reciprocal matrices is provided.

Authors 2

1. Titas Geryba Aachen Mathematisch Instituut

   Leiden University

   Affiliation as printed

   Mathematisch Instituut, Universiteit Leiden, Leiden, Netherlands

2. Ilya M. Spitkovsky corresponding

   New York University Abu Dhabi

   Affiliation as printed

   Division of Science and Mathematics, New York University Abu Dhabi (NYUAD), Abu Dhabi, United Arab Emirates