Add to ORKGThe totality of normalized density matrices of dimension N forms a convex set QN in RN2−1. Working with the flat geometry induced by the Hilbert–Schmidt distance, we consider images of orthogonal projections ofQN onto a two-plane and show that they are similar to the numerical ranges of matrices of dimension N. For a matrix A of dimension N, one defines its numerical shadow as a probability distribution supported on its numerical range W(A), induced by the unitarily invariant Fubini–Study measure on the complex projective manifold CPN−1. We define generalized, mixed-state shadows of A and demonstrate their usefulness to analyse the structure of the set of quantum states and unitary dynamics therein. PACS numbers: 02.10.Yn, 02.30.Tb, 03.67.−...