In fluids applications, the size of a snapshot, M , is assumed to be much larger than the number of snapshots N , so there are many equally valid choices of A . The original DMD algorithm picks A so that each of the snapshots in V 2 N can be expressed as linear combinations of the snapshots in V 1 N − − 1 . Because most of the snapshots appear in both data sets, this representation is error free for all snapshots except v N , which is written as