where r is the vector of residuals that accounts for behaviors that cannot be described completely by A , e N − − 1 = { 0 , 0 , … … , 1 } ∈ ∈ R N − − 1 , V 1 N − − 1 = { v 1 , v 2 , … … , v N − − 1 } , and V 2 N = { v 2 , v 3 , … … , v N } . Regardless of the approach, the output of DMD is the eigenvalues and eigenvectors of A , which are referred to as the DMD eigenvalues and DMD modes respectively.