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[needs IPA] (German: Quaternionenadler; Italian: aquila quaternione), also known as the Imperial Quaternion Eagle (German: Quaternionen-Reichsadler)...

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

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

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

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 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 {...

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...

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

the complex quaternions a composition algebra. A real non-zero quaternion always has real positive norm, but a non-zero complex quaternion can have a norm...

In mathematics, a versor is a quaternion of norm one, also known as a unit quaternion. Each versor has the form u = exp ⁡ ( a r ) = cos ⁡ a + r sin ⁡...

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 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...

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

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...

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

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...

founded in the Province of Canada. 1843 – William Rowan Hamilton invents quaternions, a three-dimensional system of complex numbers. 1846 – William T. G....

announced to his mathematician friend William Hamilton, discoverer of quaternions, in a letter on this date. 1860 – First Rules derby is held between Sheffield...

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

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

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

career included the analysis of geometrical optics, Fourier analysis, and quaternions, the last of which made him one of the founders of modern linear algebra...

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...

:\|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...