  The saturation theorem of [Knutson-Tao '99] concerns the nonvanishing of
Littlewood-Richardson coefficients. In combination with work of [Klyachko '98],
it implies [Horn '62]'s conjecture about eigenvalues of sums of Hermitian
matrices. This eigenvalue problem has a generalization [Friedland '00] to
majorized sums of Hermitian matrices.
  We further illustrate the common features between these two eigenvalue
problems and their connection to Schubert calculus of Grassmannians. Our main
result gives a Schubert calculus interpretation of Friedland's problem, via
equivariant cohomology of Grassmannians. In particular, we prove a saturation
theorem for this setting. Our arguments employ the aformentioned work together
with [Thomas-Yong '12].
