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In fluid mechanics, modal decomposition, deeply intertwined with the concept of symmetry, is an essential data analysis method. It facilitates the segmentation of parameters such as flow, velocity, and pressure fields into distinct modes, each exhibiting symmetrical or asymmetrical characteristics in terms of amplitudes, frequencies, and phases. This technique, emphasizing the role of symmetry, is pivotal in both theoretical research and practical engineering applications. This paper delves into two dominant modal decomposition methods, infused with symmetry considerations: Proper Orthogonal Decomposition (POD) and Dynamic Mode Decomposition (DMD). POD excels in dissecting flow fields with clear periodic structures, often showcasing symmetrical patterns. It utilizes basis functions and time coefficients to delineate spatial modes and their evolution, highlighting symmetrical or asymmetrical transitions. In contrast, DMD effectively analyzes more complex, often asymmetrical structures like turbulent flows. By performing iterative analyses on the flow field, DMD discerns symmetrical or asymmetrical statistical structures, assembling modal functions and coefficients for decomposition. This method is adapted to extracting symmetrical patterns in vibration frequencies, growth rates, and intermodal coupling. The integration of modal decomposition with symmetry concepts in fluid mechanics enables the effective extraction of fluid flow features, such as symmetrically or asymmetrically arranged vortex configurations and trace evolutions. It enhances the post-processing analysis of numerical simulations and machine learning approaches in flow field simulations. In engineering, understanding the symmetrical aspects of complex flow dynamics is crucial. The dynamics assist in flow control, noise suppression, and optimization measures, thus improving the symmetry in system efficiency and energy consumption. Overall, modal decomposition methods, especially POD and DMD, provide significant insights into the symmetrical and asymmetrical analysis of fluid flow. These techniques underpin the study of fluid mechanics, offering crucial tools for fluid flow control, optimization, and the investigation of nonlinear phenomena and propagation modes in fluid dynamics, all through the lens of symmetry. [ABSTRACT FROM AUTHOR]