# 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.
Kyrchei, "Determinantal representations of the Drazin and W-weighted Drazin inverses over the quaternion skew field with applications," in Quaternions: Theory and Applications, S.
According to the singularity of Euler angles in the presence of gimbal lock, such algorithm is replaced by the optimization from a quadratic nonlinear system of quaternions. The Gauss-Newton algorithm (GNA) is applied to obtain the solution of the system .
It uses special properties of quaternions to perform rotations of data sequences in 3D space for each of the cipher rounds.
Let [phi] : Z [right arrow] [Z.sub.2] be the quotient map, [phi](n), n [member of] Z will be abbreviated n and should not be confused with [bar.p], p [member of] H(R) the conjugate of the quaternions. Notice that [phi] will be used also as the obvious extension map from the matrix sets [M.sub.n](Z) to [M.sub.n]([Z.sub.2]).
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.
Quaternions avoid these singularities by having a fourth element.
The notation H will be reserved--in honor of Hamilton--for the field of quaternions; see .