In mathematics, the quaternion number system extends the complex numbers. Quaternions were first described by the Irish mathematician William Rowan Hamilton...

Unit quaternions, known as versors, provide a convenient mathematical notation for representing spatial orientations and rotations of elements in three...

angles and unit quaternions. This article explains how to convert between the two representations. Actually this simple use of "quaternions" was first presented...

In mathematics, a Hurwitz quaternion (or Hurwitz integer) is a quaternion whose components are either all integers or all half-integers (halves of odd...

quaternion in Wiktionary, the free dictionary. The quaternions form a number system that extends the complex numbers. Quaternion rotation Quaternion group...

The Quaternion Eagle (German: Quaternionenadler; Italian: Aquila Quaternione), also known as the Imperial Quaternion Eagle (German: Quaternionen-Reichsadler)...

In group theory, the quaternion group Q8 (sometimes just denoted by Q) is a non-abelian group of order eight, isomorphic to the eight-element subset {...

In mathematics, quaternions are a non-commutative number system that extends the complex numbers. Quaternions and their applications to rotations were...

Quaternion is a poetry style in which the theme is divided into four parts. Each part of a quaternion explores the complementary natures of the theme...

In mathematics, the dual quaternions are an 8-dimensional real algebra isomorphic to the tensor product of the quaternions and the dual numbers. Thus...

In abstract algebra, the algebra of hyperbolic quaternions is a nonassociative algebra over the real numbers with elements of the form q = a + b i + c...

representing a rotation as numbers in a computer, some people prefer the quaternion representation or the axis+angle representation, because they avoid the...

In mathematics, a quaternion algebra over a field F is a central simple algebra A over F that has dimension 4 over F. Every quaternion algebra becomes a...

In abstract algebra, the split-quaternions or coquaternions form an algebraic structure introduced by James Cockle in 1849 under the latter name. They...

Bench of the Rhine. The so-called imperial quaternions (German: Quaternionen der Reichsverfassung "quaternions of the imperial constitution"; from Latin...

spherical linear interpolation, introduced by Ken Shoemake in the context of quaternion interpolation for the purpose of animating 3D rotation. It refers to constant-speed...

In differential geometry, a quaternion-Kähler manifold (or quaternionic Kähler manifold) is a Riemannian 4n-manifold whose Riemannian holonomy group is...

In mathematics, a versor is a quaternion of norm one (a unit quaternion). Each versor has the form q = exp ⁡ ( a r ) = cos ⁡ a + r sin ⁡ a , r 2 = − 1...

The Quaternion Society was a scientific society, self-described as an "International Association for Promoting the Study of Quaternions and Allied Systems...

axis–angle representation. Other widely used methods include rotation quaternions, rotors, Euler angles, or rotation matrices. More specialist uses include...

left and right-handed 4 × 4 quaternion matrices is equivalent to including a single right-multiplication by a unit quaternion which adds an extra SU(2)...

The quaternion estimator algorithm (QUEST) is an algorithm designed to solve Wahba's problem, that consists of finding a rotation matrix between two coordinate...

minimize the RMSD. Coutsias, et al. presented a simple derivation, based on quaternions, for the optimal solid body transformation (rotation-translation) that...

rendition of the coat of the empire was the "Quaternion Eagle" (so named after the imperial quaternions) printed by David de Negker of Augsburg, after...

unit quaternions. Multiplication of rotation matrices is homomorphic to multiplication of quaternions, and multiplication by a unit quaternion rotates...

folded sheets of vellum or parchment, i.e. 8 leaves, 16 sides. The term quaternion (or sometimes quaternum) designates such a unit. A gathering made of a...

Hurwitz quaternions, which are the analog of integers for quaternions. Proof using the Hurwitz integers The Hurwitz quaternions consist of all quaternions with...

the study of functions with quaternions as the domain and/or range. Such functions can be called functions of a quaternion variable just as functions of...

Hamilton invented quaternions, a mathematical entity in 1843. This article describes Hamilton's original treatment of quaternions, using his notation...

:\|q\|=1\right\}.} This description as the quaternions of norm one identifies the 3-sphere with the versors in the quaternion division ring. Just as the unit circle...