# 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, i*

^{2}=

*j*

^{2}= -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 k^{w}etwer- in the Appendix of Indo-European roots.]## quaternion

(kwəˈtɜːnɪən)*n*

**1.**(Mathematics)

*maths*a generalized complex number consisting of four components,

*x*=

*x*0 +

*x*1i +

*x*2j +

*x*3k, where

*x*,

*x*0…

*x*3 are real numbers and i

^{2}= j

^{2}= k

^{2}= –1, ij = –ji = k, etc

[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 WordsSynonyms

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Noun | 1. | quaternion - the cardinal number that is the sum of three and one |

Translations

**Quaternion**

**cuaternión**

**quaternion**

**quaternione**

**quaternion**

**kwaternion**

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