  We show in microwave measurements and computer simulations that the
contribution of each eigenchannel of the transmission matrix to the density of
states (DOS) is the derivative with angular frequency of a composite phase
shift. The accuracy of the measurement of the DOS determined from transmission
eigenchannels is confirmed by the agreement with the DOS found from the
decomposition of the field into modes. The distribution of the DOS, which
underlies the Thouless number, is substantially broadened in the Anderson
localization transition. We find a crossover from constant to exponential
scaling of fluctuations of the DOS normalized by its average value. These
results illuminate the relationships between scattering, stored energy and
dynamics in complex media.
