Dynamic Mode Decomposition (DMD) is a powerful tool for analyzing the dynamics of nonlinear systems, particularly in fluid mechanics. The paper introduces a theoretical framework that generalizes DMD to a broader class of datasets, including nonsequential time series, by defining DMD as the eigendecomposition of an approximating linear operator. This generalization enhances computational efficiency and mitigates noise effects. The authors also introduce the concept of linear consistency, which helps explain the potential pitfalls of applying DMD to rank-deficient datasets. They demonstrate that DMD is equivalent to Linear Inverse Modeling (LIM) under certain conditions and establish connections between DMD and other techniques such as the Eigensystem Realization Algorithm (ERA) and LIM. The paper provides algorithms for computing DMD modes and eigenvalues, and discusses practical applications, including nonuniform temporal sampling and combining multiple experimental runs to reduce noise. The theoretical framework and practical applications highlight the strengths and limitations of DMD in analyzing nonlinear dynamics.Dynamic Mode Decomposition (DMD) is a powerful tool for analyzing the dynamics of nonlinear systems, particularly in fluid mechanics. The paper introduces a theoretical framework that generalizes DMD to a broader class of datasets, including nonsequential time series, by defining DMD as the eigendecomposition of an approximating linear operator. This generalization enhances computational efficiency and mitigates noise effects. The authors also introduce the concept of linear consistency, which helps explain the potential pitfalls of applying DMD to rank-deficient datasets. They demonstrate that DMD is equivalent to Linear Inverse Modeling (LIM) under certain conditions and establish connections between DMD and other techniques such as the Eigensystem Realization Algorithm (ERA) and LIM. The paper provides algorithms for computing DMD modes and eigenvalues, and discusses practical applications, including nonuniform temporal sampling and combining multiple experimental runs to reduce noise. The theoretical framework and practical applications highlight the strengths and limitations of DMD in analyzing nonlinear dynamics.