2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/66359We characterize the relationship between the singular values of a complex Hermitian (resp., real symmetric, complex symmetric) matrix and the singular values of its off-diagonal block. We also characterize the eigenvalues of an Hermitian (or real symmetric) matrix C=A+B in terms of the combined list of eigenvalues of A and B. The answers are given by Horn-type linear inequalities. The proofs depend on a new inequality among Littlewood-Richardson coefficients.24 pages. This is the final version, to appear in American Journal of MathematicsAlgebraic GeometryRings and Algebras15A42; 05E15; 14M15; 15A18text