Definitions for versor

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Webster Dictionary

  1. Versor(noun)

    the turning factor of a quaternion


  1. Versor

    In quaternion algebra, a versor or unit quaternion is a quaternion of norm one. Every versor is of the form Such a versor may be viewed as a directed great-circle arc with axis r and length a. In case a = π/2, the versor is a right versor. In linear algebra, geometry, and physics, the term versor is often used for a right versor. Left multiplication qz of a quaternion z to a versor q is identical to the action of the special unitary group SU on the 2-dimensional complex space; hence, quaternionic versors are the traditional term and presentation for elements of SU. When used to represent a 3-dimensional rotation, a versor will rotate any quaternion vector v through the angle θ around the unit vector r through the sandwiching product qvq−1. The word is from Latin versus = "turned", from pp. of vertere = "to turn", and was introduced by William Rowan Hamilton, in the context of his quaternion theory.


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