  Horn's problem was the following: given two Hermitian matrices with known
spectra, what might be the eigenvalue spectrum of the sum? This linear algebra
problem is exactly of the sort to be approached with the methods of modern
Hamiltonian geometry (which were unavailable to Horn). The theorem linking
symplectic quotients and geometric invariant theory lets one also bring
algebraic geometry and representation theory into play. This expository note is
intended to elucidate these connections for linear algebraists, in the hope of
making it possible to recognize what sort of problems are likely to fall to the
same techniques that were used in proving Horn's conjecture.
