# Definitions for **quaternion**kwəˈtɜr ni ən

### This page provides all possible meanings and translations of the word **quaternion**

### Random House Webster's College Dictionary

qua•ter•ni•onkwəˈtɜr ni ən(n.)

a group or set of four persons or things.

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.

**Category:**Math

#### Origin of **quaternion**:

1350–1400; ME quaternioun < LL quaterniō= L quatern(ī) four at a time +-iō -ion

### Princeton's WordNet

four, 4, IV, tetrad, quatern, quaternion, quaternary, quaternity, quartet, quadruplet, foursome, Little Joe(noun)

the cardinal number that is the sum of three and one

### Wiktionary

quaternion(Noun)

A group or set of four people or things.

quaternion(Noun)

A four-dimensional hypercomplex number that consists of a real dimension and 3 imaginary ones (i, j, k) that are each a square root of -1. They are commonly used in vector mathematics and in calculating the rotation of three-dimensional objects.

### Webster Dictionary

Quaternion(noun)

the number four

Quaternion(noun)

a set of four parts, things, or person; four things taken collectively; a group of four words, phrases, circumstances, facts, or the like

Quaternion(noun)

a word of four syllables; a quadrisyllable

Quaternion(noun)

the quotient of two vectors, or of two directed right lines in space, considered as depending on four geometrical elements, and as expressible by an algebraic symbol of quadrinomial form

Quaternion(verb)

to divide into quaternions, files, or companies

### Freebase

Quaternion

In mathematics, the quaternions are a number system that extends the complex numbers. They were first described by Irish mathematician William Rowan Hamilton in 1843 and applied to mechanics in three-dimensional space. A feature of quaternions is that the product of two quaternions is noncommutative. Hamilton defined a quaternion as the quotient of two directed lines in a three-dimensional space or equivalently as the quotient of two vectors. Quaternions can also be represented as the sum of a scalar and a vector. Quaternions find uses in both theoretical and applied mathematics, in particular for calculations involving three-dimensional rotations such as in three-dimensional computer graphics and computer vision. They can be used alongside other methods, such as Euler angles and rotation matrices, or as an alternative to them depending on the application. In modern mathematical language, quaternions form a four-dimensional associative normed division algebra over the real numbers, and thus also form a domain. In fact, the quaternions were the first noncommutative division algebra to be discovered. The algebra of quaternions is often denoted by H, or in blackboard bold by . It can also be given by the Clifford algebra classifications Cℓ0,2 ≅ Cℓ03,0. The algebra H holds a special place in analysis since, according to the Frobenius theorem, it is one of only two finite-dimensional division rings containing the real numbers as a proper subring, the other being the complex numbers.³

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"quaternion." *Definitions.net.* STANDS4 LLC, 2014. Web. 26 Nov. 2014. <http://www.definitions.net/definition/quaternion>.