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 Indo-European roots.]
American Heritage® Dictionary of the English Language, Fifth Edition. Copyright © 2016 by Houghton Mifflin Harcourt Publishing Company. Published by Houghton Mifflin Harcourt Publishing Company. All rights reserved.

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]
Random House Kernerman Webster's College Dictionary, © 2010 K Dictionaries Ltd. Copyright 2005, 1997, 1991 by Random House, Inc. All rights reserved.
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
IV, Little Joe, quadruplet, quartet, quatern, 4, four, quaternity, tetrad, foursome, quaternary
digit, 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
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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.
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Bahri, "Quaternion algebra-valued wavelet transform," Applied Mathematical Sciences, vol.
A Version of Uncertainty Principle for Quaternion Linear Canonical Transform
over the complex field, a principle domain, and the quaternion skew field has been actively ongoing for many years.
Determinantal Representations of Solutions and Hermitian Solutions to Some System of Two-Sided Quaternion Matrix Equations
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.
Linear BVPs and SIEs for Generalized Regular Functions in Clifford 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 [34]:
An Indoor Navigation System Based on Stereo Camera and Inertial Sensors with Points and Lines
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].
Linear systems over Z[[Q.sub.16]] and roots of maps of some 3-complexes into [mathematical expression not reproducible]
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.
CH. S. PEIRCE'S PHANEROSCOPY AS EARLY COMMUNICOLOGY/CH. S. PEIRCE'O FANEROSKOPIJA KAIP ANKSTYVOJI KOMUNIKOLOGIJA
[8], embeds watermark bits in the hypercomplex domain using the quaternion Fourier transform (QFT) coefficients.
A perceptually-adaptive high-capacity color image watermarking system
We exploit quaternion calculated from readings of these three sensors for accurate angle estimation.
Real-Time Fall Risk Assessment Using Functional Reach Test
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.
Generation and Control of Basic Geometric Trajectories for a Robot Manipulator Using CompactRIO[R]
The rotation matrix and the unit quaternion are examples of constrained parameterizations.
Multitemporal Volume Registration for the Analysis of Rheumatoid Arthritis Evolution in the Wrist

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