Elliptic numerical range of matrices

Abstract

The numerical range W ( T ) of a complex n × n matrix T is the subset W ( T ) = {(cid:104) T x, x (cid:105) : x ∈ C n , and (cid:107) x (cid:107) = 1 } in the complex plane C , where (cid:104) ., . (cid:105) denotes the usual inner product in C . In this paper a series of tests given, allowing one to determine when the numerical range of a 6 × 6 matrix T is an elliptic disc.