# Versor

## Definitions

• Webster's Revised Unabridged Dictionary
• n Versor (Geom) The turning factor of a quaternion.☞ The change of one vector into another is considered in quaternions as made up of two operations; 1st, the rotation of the first vector so that it shall be parallel to the second; 2d, the change of length so that the first vector shall be equal to the second. That which expresses in amount and kind the first operation is a versor, and is denoted geometrically by a line at right angles to the plane in which the rotation takes place, the length of this line being proportioned to the amount of rotation. That which expresses the second operation is a tensor. The product of the versor and tensor expresses the total operation, and is called a quaternion. See Quaternion.
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Century Dictionary and Cyclopedia
• n versor A particular kind of quaternion; an operator which, applied to a vector lying in a plane related in a certain way to the versor, turns the vector through an angle without altering its modulus, tensor, or length. Every quaternion is a product, in one way only, of a tensor and a versor, and that versor is called the versor of the quaternion, and is represented by a capital U written before the symbol of the quaternion.
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## Etymology

Webster's Revised Unabridged Dictionary
NL., fr. L. vertere, versus, to turn. See Version

## Usage

### In science:

The orientation of the dual bonds must be such that the vector product between each bond and its dual bond has the same sign with respect to the normal versor outgoing from the surface.
General duality for abelian-group-valued statistical-mechanics models
We call e(i) the versors of the canonical basis of Rd .
Which random walks are cyclic?
The last direction - side - is along the vector product of the out and long versors.
Test of Bowler-Sinyukov Treatment of Coulomb Interaction
The operators appearing in (3) are the orbital ~L and spin ~S angular momenta, the position versor br = ~r/r, and the spin-transition operator ~T deﬁned here as the spin analog of br (see sect. 2.4 below for a detailed discussion of this operator).
Addition theorems for spin spherical harmonics. I Preliminaries
As in the previous case, the product of standard versors can be substituted by δkh .
Addition theorems for spin spherical harmonics. I Preliminaries
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