Before revision:  Despite their similar goal, the two methods are largely used by distinct scientific communities . For the first time, examine the two together and show that, under a certain (reasonable) condition on the data, the theoretical decomposition given by tensor component analysis is the same as that given by Koopman mode decomposition.
After revision:  Despite their similar goal, the two methods are largely used by different scientific communities and formulated in distinct mathematical languages. We examine the two together and show that, under a certain (reasonable) condition on the data, the theoretical decomposition given by tensor component analysis is the same as that given by Koopman mode decomposition.