# 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.]

## 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:
 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"
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.
Shu, "Color image watermarking based on quaternion Fourier transform and improved uniform log-polar mapping," Journal of Computers & Electrical Engineering, vol.
Each sample of the audio signal is combined with the values of the three color components of a pixel fetched from the cover image yielding a quaternion number.
As the rotation data provided by Hector SLAM is in the quaternion format ([q.
2), generalized quaternion groups (, Corollary 1), torsion-free divisible Abelian groups (, Theorem 1), etc.
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.
8], embeds watermark bits in the hypercomplex domain using the quaternion Fourier transform (QFT) coefficients.
They are Rolls-Royce, Thales, Microturbo (Safran), Liebherr, OPAL-RT, Quaternion Aerospace, FusiA, Axis, the University of Victoria, Ryerson University, the University of Toronto, McGill University, National Research Council Canada, and Polytechnique Montral.
Therefore, each client PC converts the quaternion to rotation matrix
First attempts to this were done by Pita, del Rio and Ruiz in [16,17], where the authors use Ford domains to get presentations of some small subgroups of congruence subgroups of Bianchi groups and by Corrales, Jespers, Leal and del Rio in , where a presentation for the unit group of a "small" non-commutative division algebra (a quaternion algebra) is given using Dirichlet domains.
This is the main idea for sensor fusion using quaternion representation.
It allows for user-programmable tuning and provides individual sensor outputs via SPI, as well as specialized data such as quaternion, Euler, and rotation matrices.

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