Diameter and minimal width of the numerical range
Nam-Kiu Tsin · Linear and Multilinear Algebra · 1983
Let V be an n-dimensional unitary space and S the set {x ε V: x*x =1}. For any Aϵ Hom(V, V), the numerical range of A is defined to be the set W (A) = {x * Ax : xϵS), the convexity of which is well-known. In this note, we consider the set E(A) = {x*Ay + y*Ax : x, y ϵ S, y*x = 0} and discuss its relation with W(A). We also give a characterization of the diameter and the minimal width of W(A).