  We 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.
