# 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 periodicals archive ?
The chirality context drives the way the real differential of a map may be written as the sum of two parts which, roughly speaking, behave as the real and the imaginary part of a quaternion: the composition of maps is shown to have exactly the same algebraic structure as the product of quarternions. In this picture, the main result states that regularity is the same as having a purely imaginary differential, so that the bad properties of regularity simply mirror the unavoidable and widely accepted properties of the imaginary quaternions: the unit is not imaginary, nor is the product of imaginary quaternions, in general.
I am totally unconvinced that Dodson was specifically satirizing the Symbolic Logic of George Boole and Augustus De Morgan, or the Projective Geometry of Poncelet, or the Quarternions of Wm.

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