In this form, DMD is a type of Arnoldi method, and therefore the eigenvalues of S are approximations of the eigenvalues of A . Furthermore, if y is an eigenvector of S , then V 1 N − − 1 y is an approximate eigenvector of A . The reason an eigendecomposition is performed on S rather than A is because S is much smaller than A , so the computational cost of DMD is determined by the number of snapshots rather than the size of a snapshot.