Assume we start with 2D data matrix, $Z$, with dimensions R and T. (R is space, T is time).

Define $X=Z(t)$ and $X'=Z(t+dt)$

Perform SVD on X to get spatial basis functions. $U,S,V^T = \text{SVD}(X)$

Define $A=(U^T \cdot X') \cdot \left (\frac{V}{S} \right)$

Find eivenvalues and eigenvectors. $\lambda, v = \text{eig} (A)$

spatial structure. $Bt = \left(X' \cdot \frac{V}{S} \right) \cdot v$

$\omega = \frac{ \text{log} \left| \lambda \right| }{dt}$

time evolution. Vandermonde, $M = e^{\omega \otimes t}$