In this paper, the mathematical relationships between matrix-formatted frequency-domain fluorescence decay data and the photokinetic transfer matrix are derived. These relationships reveal that procedures for analyzing the fluorescence spectra and photokinetic mechanism of excited state reactions without model assumptions can be developed when the fluorescence decay is described by first-order differential equations with constant coefficients and when the spectral emission profiles of the decaying fluorophores are distinct. The linear structure of wavelength-dependent frequency-domain decay data permits the simultaneous estimation of the emission spectra, relative initial concentrations, and the photokinetic transfer matrix describing the decay and interaction of multiple fluorophores. Data matrices acquired using a single sample are amenable to this approach, eliminating the necessity to measure probe lifetimes separately at low fluorophore concentration. Most importantly, this method does not require that the analyst choose a kinetic model describing fluorophore emission. Instead, the kinetic mechanism is revealed in the structure of the transfer matrix. Statistical methods can be used to estimate the number of emitting components contributing to a data matrix, so that every aspect of the analysis can be pursued without a priori assumptions. Other analytical tools, including a procedure for matrix partitioning to estimate the spectra of sample fluorophores when the spectra are unknown and graphical tools for evaluating prospective spectra and decays, also are described.