# Dynamic Mode Decomposition and Koopman Theory

arXiv: https://arxiv.org/abs/2211.07561 · HTML: https://mlsanity.com/paper/2211.07561/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 14 Nov 2022.

## Built on by (most cited first, 2 of 2)

- [DLKoopman: A deep learning software package for Koopman theory](https://mlsanity.com/paper/2211.08992/) (2022)
- [Optimal Derivative Feedback Control for an Active Magnetic Levitation System: An Experimental Study on Data-Driven Approaches](https://mlsanity.com/paper/2602.06944/) (2026)

## Abstract (arXiv)

Dynamic Mode Decomposition (DMD) is a technique to approximate generally non-linear dynamical systems using linear techniques, which are better understood and easier to analyze. Koopman theory extends DMD by transforming the original system into a new domain which facilitates linearization. This is a technical report on DMD and Koopman theory, with primary focus on explaining the underlying mathematics in clear and concise form. We include dimensions of vectors and marices, and step-by-step derivations of equations in order to assist the user in easily comprehending these concepts. This report will also enable users to implement DMD and Koopman theory in code.