  We study the relation between the spectrum of a self-adjoint operator and its
multidimensional numerical range. It turns out that the multidimensional
numerical range is a convex set whose extreme points are sequences of
eigenvalues of the operator. Every collection of eigenvalues which can be
obtained by the Rayleigh--Ritz formula generates an extreme point of the
multidimensional numerical range. However, it may also have other extreme
points.
