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The letters SO with a dimension in brackets, the rotations of a space.
Also known as: Special orthogonal group, Rotation group, SO
SO(3) is exactly the set of rotations of ordinary three-dimensional space. The 'special' means determinant one, which excludes reflections — so SO(3) is rotations only, while O(3) also contains every mirror image.
Denotes the special orthogonal group: the orthogonal matrices of determinant one, which are the rotations of a Euclidean space.
Contexts: Mathematics
Differs from the orthogonal group O(n) exactly by excluding the determinant-minus-one elements, which are the reflections.
Contexts: Mathematics
SO(3) is the configuration space of a rigid body's orientation, which is why it appears throughout robotics and spacecraft attitude work.
Contexts: Mathematics
Two capital letters S and O followed by a bracketed numeral.