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...

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

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

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

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

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

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, 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...

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...

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

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 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...

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

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...

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

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

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

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

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

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

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

the dual quaternion algebra to 2D geometry. At this present time, the article is focused on a 4-dimensional subalgebra of the dual quaternions which we...

In differential geometry, a quaternion-Kähler symmetric space or Wolf space is a quaternion-Kähler manifold which, as a Riemannian manifold, is a Riemannian...

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...

variants thereof, and the elements of {1, i, j, k} multiply as in the quaternion group and commute with their coefficients. There are three types of biquaternions...

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

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...