Finite-amplitude, unstable, time-periodic solutions of a two-layer, 48x40-mode spectral, quasi-geostrophic channel model are computed and analyzed. The solutions consist of nonlinear life-cycles of baroclinic waves, which grow to large amplitude, decay to nearly zonal flow, and then grow again. The evolution of linear disturbances to these flows is completely described by the associated Floquet vectors, which are the normal modes of the time-dependent basic flow and the analog of Lyapunov vectors for time-periodic basic flows, and which take the form of the product of an exponential growth or decay term and a time-periodic spatio-temporal structure function that undergoes a complex evolution during the wave cycle. The Floquet vectors are amenable to dynamical interpretation and analysis. Singular vectors and analogs of bred vectors are computed directly from the Floquet vectors. Results of these analyses are presented and discussed, and related to previous results for weakly nonlinear baroclinic waves. Consequences of the results for the design of ensemble generation methods are emphasized.