versor

The common norm of a versor is always equal to positive unity.

A versor is a quaternion with a tensor of 1.

In words the reciprocal of a versor is equal to its conjugate.

A versor has an easy formula for its reciprocal.

In the former case the versor is circular, in the latter hyperbolic.

It can also be represented as the product of its tensor and its versor.

Reciprocals have many important applications, for example rotations, particularly when q is a versor.

Any unit quaternion q can be written as a versor:

In mathematics, versor is a quaternion of norm 1, an algebraic rotation representation.

Alternatively, a versor can be defined as the quotient of two equal-length vectors.

Hamilton denoted the versor of a quaternion q by the symbol Uq.

Decompose the vector part further as the product of its norm and its versor:

With the further development of special relativity the action of a hyperbolic versor came to be called a Lorentz boost.

Thus a versor is sometimes defined as a unit vector indicating the direction of a directed axis or vector.

The Latin term for turn is versor, which is a quaternion that can be visualized as an arc of a great circle.

The rapidity parameter amounts to the length of a hyperbolic versor, a concept of the nineteenth century.

Every quaternion is equal to a versor multiplied by the tensor of the quaternion.

An example of a one-parameter group is the hyperbolic versor with the hyperbolic angle parameter.

Versor (who overthrows or who pours rain)

In special relativity, the hyperbolic angle parameter of a hyperbolic versor is called rapidity.

At Paris he studied with John Versor, and would receive philosophical training according to the trend of "Albertism."

In quaternion algebra, a versor or unit quaternion is a quaternion of norm one.

In linear algebra, geometry, and physics, the term versor is often used for a right versor.

A hyperbolic versor is a generalization of quaternionic versors to indefinite orthogonal groups, such as Lorentz group.

In general a versor defines all of the following: a directional axis; the plane normal to that axis; and an angle of rotation.