Georgia Institute of Technology College of Sciences

The Horn inequalities give a characterization of eigenvalues of self-adjoint n by n matrices A, B, C with A+B+C=0. The original proof by Klyachko and Knutson-Tao, requires tools from algebraic geometry, among other things. Our recent work provides a proof using only elementary tools that made it possible to generalize the Horn inequalities to finite von Neumann factors. No knowledge of von Neumann algebra is required.