quaternion


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qua·ter·ni·on

 (kwə-tûr′nē-ən)
n.
1. A set of four persons or items.
2. Mathematics Any number of the form a + bi + cj + dk where a, b, c, and d are real numbers, ij = k, i2 = j2 = -1, and ij = -ji. Under addition and multiplication, quaternions have all the properties of a field, except multiplication is not commutative.

[Middle English quaternioun, from Late Latin quaterniō, quaterniōn-, from Latin quaternī, by fours, from quater, four times; see kwetwer- in the Appendix of Indo-European roots.]

quaternion

(kwəˈtɜːnɪən)
n
1. (Mathematics) maths a generalized complex number consisting of four components, x = x0 + x1i + x2j + x3k, where x, x0…x3 are real numbers and i2 = j2 = k2 = –1, ij = –ji = k, etc
2. another word for quaternary5
[C14: from Late Latin quaterniōn, from Latin quaternī four at a time]

qua•ter•ni•on

(kwəˈtɜr ni ən)

n.
1. a group or set of four persons or things.
2. a generalization of a complex number to four dimensions with three different imaginary units in which a number is represented as the sum of a real scalar and three real numbers multiplying each of the three imaginary units.
[1350–1400; Middle English quaternioun < Late Latin quaterniō= Latin quatern(ī) four at a time + -iō -ion]
ThesaurusAntonymsRelated WordsSynonymsLegend:
Noun1.quaternion - the cardinal number that is the sum of three and onequaternion - the cardinal number that is the sum of three and one
digit, figure - one of the elements that collectively form a system of numeration; "0 and 1 are digits"
Translations
Quaternion
cuaternión
quaternion
quaternione
quaternion
kwaternion
References in classic literature ?
Aire, and ye Elements the eldest birth Of Natures Womb, that in quaternion run Perpetual Circle, multiform; and mix And nourish all things, let your ceasless change Varie to our great Maker still new praise.
Thus, we have a unit quaternion group PSL(2,C) (equivalently, an SU(2) matrix or spinor) representation of the Lorentz transformation.
This collection of 26 articles includes those from peer-reviewed journals that give background to such questions as the nature of Tifft redshift and generalized Schrodinger equations; Weyle geometry, extended relativity, supersymmetry and their applications in astrophysics; the phion condensate, including five articles authored or co-authored by Christianto; Cartan-Weyl space time, torsion fields and Navier-Stokes; and the hypergeometrical universe, pioneer anomalies and quaternion relativity.
The newest release continues to advance character animation techniques and motion capture tools in ways never thought possible with the addition of a constraint-based animation mixer, an animation analyzer and fixer and Quaternion Function Curves.
Quaternion space and its respective Quaternion Relativity (it also may be called as Rotational Relativity has been defined in a number of papers including [1], and it can be shown that this new theory is capable to describe relativistic motion in elegant and straightforward way.
character studio 4 -- The upcoming extension package for Discreet 3ds max software contains significant new features including nonlinear animation mixer, industry-first Quaternion function curves, and an animation analyzer and fixer that identifies the finer aspects of an animation for correction.
We can note here, for instance, that Yang-Mills field somehow can appear more or less quite naturally if one uses quaternion or hypercomplex numbers as basis.
In this paper we write the Maxwell equations in quaternion including the Lorentz force and the continuity equation.
We have recently shown that quaternion equation (Arbab and Satti, 2009 [1])
New character animation features include easy FK/IK switching, switchable Euler and Quaternion rotations, motion trails and ghosting along with a powerful new Jiggle Deformer which automatically creates secondary "character fat/muscle wobble" animation without dynamics.
In the light of another paper suggesting that Maxwell equations can be written using quaternion numbers, then we discuss a plausible extension of Proca equation using biquaternion number.
3] are quaternion imaginary units obeying (with ordinary quaternion symbols [e.