2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/78911We 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 $GL_n(\mathbb{C})$. 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.42 pages, AMSTeX, with Xy-pic. This is the final version, including corrections made in page proofs for publication as a Research/Expository article in Bull. Amer. Math. SocAlgebraic GeometryCommutative AlgebraRepresentation Theory15A42; 22E46; 14M15; 05E15; 13F10; 14C17; 15A18; 47B07text