Definitions for versor
ver·sor

WikipediaRate this definition:0.0 / 0 votes

1. 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 DictionaryRate this definition:0.0 / 0 votes

1. Versornoun

   the turning factor of a quaternion

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

WikidataRate this definition:0.0 / 0 votes

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.

How to pronounce versor?

1. Alex

   US English

   David

   US English

   Mark

   US English

   Daniel

   British

   Libby

   British

   Mia

   British

   Karen

   Australian

   Hayley

   Australian

   Natasha

   Australian

   Veena

   Indian

   Priya

   Indian

   Neerja

   Indian

   Zira

   US English

   Oliver

   British

   Wendy

   British

   Fred

   US English

   Tessa

   South African

How to say versor in sign language?

Numerology

1. Chaldean Numerology

   The numerical value of versor in Chaldean Numerology is: 7

2. Pythagorean Numerology

   The numerical value of versor in Pythagorean Numerology is: 7

References

1. ^ Wikipedia
   https://en.wikipedia.org/wiki/Versor
2. ^ Webster Dictionary
   https://www.merriam-webster.com/dictionary/versor
3. ^ Wikidata
   https://www.wikidata.org/w/index.php?search=versor