In order to apply standard DMD (Schmid, 2010) to such a signal, the first-order Koopman assumption is employed, which can be written in multiple different forms: where k = 2, ..., N and A is a m × m square matrix.
the assumption is that each sentence has words in it which lie in a constant subspace generated by A (Brunton et al., 2016), or that the words in a sentence transition from one another smoothly, transformed by the constant operator A.