ABSTRACT
Several quite distinct problems in operator theory concerning eigenvalues, singular values, and Jordan models have virtually identical answers. This chapter explains how these answers can all be derived from Schubert calculus, that is, from the intersection theory of the Grassmann manifold. The connection between intersection theory and the characterization of the eigenvalues of a sum of Hermitian matrices was known for some time and was completed by the work of A. Klyachko, A. Knutson, and T. Tao. The connection with the other questions alluded to above was found more recently. The chapter discusses finite-as well as infinite-dimensional versions of these problems, some of which are not completely resolved.
