  Dynamic Mode Decomposition (DMD) is a data-driven decomposition technique
extracting spatio-temporal patterns of time-dependent phenomena. In this paper,
we perform a comprehensive theoretical analysis of various variants of DMD. We
provide a systematic advancement of these and examine the interrelations. In
addition, several results of each variant are proven. Our main result is the
exact reconstruction property. To this end, a new modification of scaling
factors is presented and a new concept of an error scaling is introduced to
guarantee an error-free reconstruction of the data.
