### What does **versor** mean?

# Definitions for versor

ver·sor

#### This dictionary definitions page includes all the possible meanings, example usage and translations of the word **versor**.

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### Wikipedia

Versor

In mathematics, a versor is a quaternion of norm one (a unit quaternion). The word is derived from Latin versare = "to turn" with the suffix -or forming a noun from the verb (i.e. versor = "the turner"). It was introduced by William Rowan Hamilton in the context of his quaternion theory. Each versor has the form q = exp ( a r ) = cos a + r sin a , r 2 = − 1 , a ∈ [ 0 , π ] , {\displaystyle q=\exp(a\mathbf {r} )=\cos a+\mathbf {r} \sin a,\quad \mathbf {r} ^{2}=-1,\quad a\in [0,\pi ],} where the r2 = −1 condition means that r is a unit-length vector quaternion (or that the first component of r is zero, and the last three components of r are a unit vector in 3 dimensions). The corresponding 3-dimensional rotation has the angle 2a about the axis r in axis–angle representation. In case a = π/2 (a right angle), then q = r {\displaystyle q=\mathbf {r} } , and the resulting unit vector is termed a right versor. The collection of versors with quaternion multiplication forms a group, and the set of versors is a 3-sphere in the 4-dimensional quaternion algebra.

### Webster Dictionary

Versornoun

the turning factor of a quaternion

**Etymology:**[NL., fr. L. vertere, versus, to turn. See Version.]

### Wikidata

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.

### Numerology

Chaldean Numerology

The numerical value of versor in Chaldean Numerology is:

**7**Pythagorean Numerology

The numerical value of versor in Pythagorean Numerology is:

**7**

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