  We measure the field transmission matrix t for microwave radiation
propagating through random waveguides in the crossover to Anderson
localization. From these measurements, we determine the dimensionless
conductance, g, and the individual eigenvalues $\tau_n$ of the transmission
matrix $tt^\dagger$ whose sum equals g. In diffusive samples, the highest
eigenvalue, $\tau_1$, is close to unity corresponding to a transmission of
nearly 100%, while for localized waves, the average of $\tau_1$, is nearly
equal to g. We find that the spacing between average values of $\ln\tau_n$ is
constant and demonstrate that when surface interactions are taken into account
it is equal to the inverse of the bare conductance.
