# 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.
Keywords: Quaternions, Cryptography, Symmetric, Asymmetric, Encryption, Decryption, Simulink.
With the aid of complex numbers, the quaternions more specifically, it will allows us to see these 10 classes and their triangles in a three-dimensional condition.
T] can be converted from quaternions using (7) expression
This is the definition of alternative algebra; according to Hurwitz theorem [10], only four exist which are R real numbers, C complex numbers ~ U(1), H quaternions ~ SU(2), and O octonions ~ SU(3).
He discusses continued fractions; the geometry of complex numbers, quaternions, and spins; and Euler groups and the arithmetic of geometric progressions.
The quaternions are used for the attitude evaluation:
If more markers are seen, the location vectors and rotation quaternions are averaged.
Many new exercises have been added, while new study projects examine skewfields, quaternions, and octonions.
In the perceptual hashing schemes proposed in the literatures [9] and [10], the input color image is represented as a pure quaternion matrix by representing the RGB components as the three imaginary parts of the pure quaternions.

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