# Rotating a Unit Vector in 3D Using Quaternions

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A quaternion is a vector in with a noncommutative product (see [1] or Quaternion (Wolfram *MathWorld*)). Quaternions, also called *hypercomplex* *numbers*, were invented by William Rowan Hamilton in 1843. A quaternion can be written or, more compactly, or , where the noncommuting unit quaternions obey the relations .

Contributed by: Gerard Balmens (February 2016)

Open content licensed under CC BY-NC-SA

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Reference

[1] Wikipedia. "Quaternions and Spatial Rotation." (Feb 9, 2016) en.wikipedia.org/wiki/Quaternions_and_spatial _rotation.

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