On eigenvalues and boundary curvature of the numerical range Original Research Article

Let A be an n×n matrix. By Donoghueʹs theorem, all corner points of its numerical range W(A) belong to the spectrum σ(A). It is therefore natural to expect that, more generally, the distance from a point p on the boundary ∂W(A) of W(A) to σ(A) should be in some sense bounded by the radius of curvature of ∂W(A) at p. We establish some quantitative results in this direction.