2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/73089We give a minimal list of inequalities characterizing the possible eigenvalues of a set of Hermitian matrices with positive semidefinite sum of bounded rank. This answers a question of A. Barvinok.Rings and AlgebrasAlgebraic Geometry15A42 (Primary) 14M15, 05E15 (Secondary)text