Markovian processes are stochastic processes where the future state of the system, x t+τ depends only on the current state, x t . Here, t is the time step, and τ is the lag time. Various Markov modeling approaches have been developed recently to extract key information for complex dynamical processes. These methods include and are not limited to Markov state models (MSMs), Markov transition models, variation approach to conformational dynamics (VAC), time-lagged independent component analysis (TICA), variational diffusion maps, and variational approach for Markov processes (VAMP). Dynamical systems often display high non-linearity in their system coordinates. To analyze non-linear and high-dimensional dynamical systems, we employ the Koopman operator, K, that linearly transforms the vector space spanned by observables in the form of time-series data generated by MD simulations. This facilitates the prediction and estimation of nonlinear dynamical properties through the traditional methods employed for linear dynamical systems. A majority of the Markovian modeling approaches exploit the fact that there exists a non-linear transformation of these features such that the dynamics can be approximated as a linear Markov model. Let χ 0 and χ 1 be the feature transformations for the trajectory coordinates x t and x t+τ respectively, and E be the expectation value such that the matrix K determines the dynamics of the system according to equation 1. According to the VAMP theory, when the subspaces spanned by the features, χ 0 and χ 1 , are identical to the top left and top right singular functions of K, we obtain the best finite-dimensional linear model.