Dynamic Mode Decomposition

PCA and ICA are inherently static techniques \\

leading eigendecomposition of A without computing A

X vectorized version of snapshot

want to compute leading r without computing a

Define Y Matrix

X Y almost identical

Y shifted over by 1t

\[X = U \Sigma V^*\] \[Y = AU \Sigma V^*\] \[U^* Y = U^* AU \Sigma V^*\] \[\tilde A = U^* Y V^*^{-1} \Sigma^{-1}\]