Rotations form curved spaces; exponentials resolve singularities
FrnkNlsn · x · 2026-08-26
Explains the relationship between rotation group SO(3) and its Lie algebra so(3): while rotations form a curved space, each is the exponential of a flat skew-symmetric matrix. The exponential map exp: so(3) → SO(3) converts instantaneous angular velocity into finite rotations, allowing robots, satellites, and geometric deep learning layers to handle orientations without singularities like gimbal lock.
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