Recursion methods such as Krylov techniques map complex dynamics to an effective non-interacting problem in one dimension. We show that the operator Krylov space for Floquet dynamics can be mapped to the dynamics of an edge operator of the one-dimensional Floquet inhomogeneous transverse field Ising model (ITFIM), where the latter, after a Jordan-Wigner transformation, is a Floquet model of non-interacting Majorana fermions, and the couplings are angles that we dub the Krylov angles. We present an application of this showing that a moment method exists where given a stroboscopic autocorrelation function, one can construct the corresponding Krylov angles, and from that the corresponding Floquet-ITFIM. Consequently, when no solutions for the Krylov angles are obtained, it indicates that the autocorrelation is not generated by unitary dynamics. We relate our approach to those developed using orthogonal polynomials on the unit circle. We present several applications such as the study of stable m-period dynamics as well as decaying dynamics in chaotic systems.