Eigenvalues, invariant factors, highest weights, and Schubert calculus

William Fulton
2000 Bulletin of the American Mathematical Society  
We describe recent work of Klyachko, Totaro, Knutson, and Tao that characterizes eigenvalues of sums of Hermitian matrices and decomposition of tensor products of representations of GLn(C). We explain related applications to invariant factors of products of matrices, intersections in Grassmann varieties, and singular values of sums and products of arbitrary matrices.
doi:10.1090/s0273-0979-00-00865-x fatcat:xn3f4xuvqzarnmrkimv6ey4tsm