# quaternion

Also found in: Thesaurus, Encyclopedia, Wikipedia.

## 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 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]
Collins English Dictionary – Complete and Unabridged, 12th Edition 2014 © HarperCollins Publishers 1991, 1994, 1998, 2000, 2003, 2006, 2007, 2009, 2011, 2014

## 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:
 Noun 1 quaternion - the cardinal number that is the sum of three and onedigit, figure - one of the elements that collectively form a system of numeration; "0 and 1 are digits"
Based on WordNet 3.0, Farlex clipart collection. © 2003-2012 Princeton University, Farlex Inc.
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.
Bahri, "Quaternion algebra-valued wavelet transform," Applied Mathematical Sciences, vol.
They have also been extended using Clifford algebra, which includes a complex field, hyperbolic algebra, and quaternion field.
over the complex field, a principle domain, and the quaternion skew field has been actively ongoing for many years.
Based on the above-mentioned work, we further solve some kinds of BVPs and SIEs in Clifford analysis as well as BVP in quaternion analysis.
The estimates of the attitude information [??] (described in the form of unit quaternion), the velocity [[??].sup.n], and the position [[??].sup.n] can be updated by the IMU measurements as follows :
Let [Q.sub.8] = (x,y|[x.sup.2] = [y.sup.2], xyx = y) be the quaternion group of order 8 and [mathematical expression not reproducible] the orbit space of the 3-sphere [S.sup.3] with respect to the action determined by the inclusion [Q.sub.8] [??] [S.sup.3].
A quaternion, thus, is an expansion of a complex number--those compound by a + bi where a and b are natural numbers and i is the imaginary unit, since i2 = -1, that is, i is the square root of minus 1 -, so w is its real part or scalar and rest of the equation is its imaginary part or vector.
, embeds watermark bits in the hypercomplex domain using the quaternion Fourier transform (QFT) coefficients.
We exploit quaternion calculated from readings of these three sensors for accurate angle estimation.
where [q.sub.m] is quaternion interpolated, [q.sub.o] is first quaternion, [q.sup.1] is second quaternion, [THETA] is the angle between the vectors [q.sub.o] and [q.sub.1], and t is the spherical interpolation between vectors [q.sub.o] and [q.sub.1] with values between 0 and 1.
The rotation matrix and the unit quaternion are examples of constrained parameterizations.

Site: Follow: Share:
Open / Close