Before revision:  This realization provides possibilities for new  algorithmic approaches to both Koopman mode decomposition and tensor component analysis, new insight into what is being captured by the tensor component analysis modes, and a "bridge" with which the two communities can more effectively communicate .
After revision:  This provides a "bridge" with which the two communities should be able to more effectively communicate. When this condition is not met, Koopman mode decomposition still provides a tensor decomposition with an algorithmic approaches to both Koopman mode decomposition and tensor component analysis, new insight into what is being captured by the tensor component analysis modes, and a "bridge" with which the two communities can more effectively communicate .