🎬What're geometric actions associated with antisymmetric tensors and symmetric tensors

The fundamental difference between these two tensor types is that they govern the two primary ways a body can be transformed in space: change in shape versus change in orientation. The symmetric tensor is entirely responsible for deformation, executing actions like stretching, compression, and shearing, which transforms a symmetric body (like the unit sphere) into a deformed shape, such as an ellipsoid. In contrast, the antisymmetric tensor is the mathematical generator of pure rotation, applying a rigid rotation that alters the body's orientation without affecting its size or inherent shape. Every general second-rank tensor can be uniquely broken down into these two components, allowing physicists and engineers to analyze complex physical phenomena-like stress or fluid dynamics-by separating the distorting forces from the rotational ones.

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