quaternion unit
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Quaternion — Quaternions, in mathematics, are a non commutative extension of complex numbers. They were first described by the Irish mathematician Sir William Rowan Hamilton in 1843 and applied to mechanics in three dimensional space. They find uses in both… … Wikipedia
Quaternion algebra — In mathematics, a quaternion algebra over a field, F , is a particular kind of central simple algebra, A , over F , namely such an algebra that has dimension 4, and therefore becomes the 2 times;2 matrix algebra over some field extension of F ,… … Wikipedia
Quaternion group — In group theory, the quaternion group is a non abelian group of order 8. It is often denoted by Q and written in multiplicative form, with the following 8 elements : Q = {1, −1, i , − i , j , − j , k , − k }Here 1 is the identity element, (−1)2 … Wikipedia
Quaternion-Kähler manifold — In differential geometry, a quaternion Kähler manifold (or quaternionic Kähler manifold) is a Riemannian manifold whose Riemannian holonomy group is a subgroup of Sp( n )·Sp(1). Another, more explicit, definition, uses a 3 dimensional subbundle H … Wikipedia
The vector of a quaternion — In the 19th century, the vector of a quaternion written Vq was a well defined mathematical entity in the classical quaternion notation system. This article is written using classical nomenclature. In this article the word vector means the… … Wikipedia
Dual quaternion — The set of dual quaternions is an algebra that can be used to represent spatial rigid body displacements.[1] A dual quaternion is an ordered pair of quaternions  = (A, B) and therefore is constructed from eight real parameters. Because rigid… … Wikipedia
Split-quaternion — Coquaternion multiplication × 1 i j k 1 1 i j k i i −1 k −j j j −k +1 −i … Wikipedia
Generalized quaternion interpolation — is an interpolation method used by the slerp algorithm. It is closed form and fixed time, but it cannot be applied to the more general problem of interpolating more than two unit quaternions.Definition of unconstrained interpolationGeneral… … Wikipedia
Quaternions and spatial rotation — Unit quaternions provide a convenient mathematical notation for representing orientations and rotations of objects in three dimensions. Compared to Euler angles they are simpler to compose and avoid the problem of gimbal lock. Compared to… … Wikipedia
Classical Hamiltonian quaternions — For the history of quaternions see:history of quaternions For a more general treatment of quaternions see:quaternions William Rowan Hamilton invented quaternions, a mathematical entity in 1843. This article describes Hamilton s original treatment … Wikipedia
History of quaternions — This article is an indepth story of the history of quaternions. It tells the story of who and when. To find out what quaternions are see quaternions and to learn about historical quaternion notation of the 19th century see classical quaternions… … Wikipedia
