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The rotation group is a Lie group of rotations about a fixed point. This (common) fixed point or center is called the center of rotation and is usually identified with the origin. The rotation group is a point stabilizer in a broader group of (orientation-preserving) motions. For a particular rotation: The axis of rotation is a line of … See more
Rotation in mathematics is a concept originating in geometry. Any rotation is a motion of a certain space that preserves at least one point. It can describe, for example, the motion of a rigid body around a fixed point. … See more
Rotations define important classes of symmetry: rotational symmetry is an invariance with respect to a particular rotation. The circular symmetry is an invariance with … See more
In Euclidean geometry
A motion of a Euclidean space is the same as its isometry: it leaves the distance between any two … See moreThe complex-valued matrices analogous to real orthogonal matrices are the unitary matrices $${\displaystyle \mathrm {U} (n)}$$, which represent rotations in complex space. The set of all unitary matrices in a given dimension n forms a unitary group See more
Wikipedia text under CC-BY-SA license WEBNov 21, 2023 · An object's center of rotation is defined as the point around which the object is rotated. This center of rotation definition might sound simple, but the term is different from other...
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