# 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 [15].
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 [8].
Madgwick, "Quaternions," 2011, http://x-io.co.uk/res/doc/ quaternions.pdf.
For this, the orientation and rotation must first be represented in four dimensions or quaternions and then interpolated by the method SLERP.
Both Euler angles and unit quaternions are proven to have a corresponding rotation matrix.
In the preliminaries we remind the reader of some facts of quaternions, the quaternion Fourier transform, and the quaternion linear canonical transform.

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