Some Geometrical Properties of thec-Numerical Range of a Normal Matrix
Natália Bebiano, João da Providência · Linear and Multilinear Algebra · 1994
Let A be and nxn normal matrix and C=(γ1,…,γ n ) t ∊C r . The c-numerical range, denoted by Wr (A), is the set of the points , where x1 ,…xn run over all the orthonormal complex columns. In 1988, we showed that at 2-regular points, ∂Wc (A), the boundary of Wc (A), is locally concave. In this note, a simpler proof of this fact is presented. We also prove a result concerning boundary line segments. Moreover, the lateral tangents to ∂Wc (A) at the corners are characterized.