# Quaternion definition

kwə-tûrnē-ən
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 that multiplication is not commutative.
A set of four persons or items.
noun
(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.
noun
A set of four.
noun
(math.) An expression that is the sum of four terms, one of which is real and three of which contain imaginary units, and that can be written as the sum of a scalar and a three-dimensional vector.
noun
A group or set of four people or things.
noun
A word of four syllables.
noun
(mathematics) 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.
noun

Singular:
quaternion
Plural:
quaternions

## Origin of quaternion

• Middle English quaternioun from Late Latin quaterniō quaterniōn- from Latin quaternī by fours from quater four times kwetwer- in Indo-European roots

### From American Heritage Dictionary of the English Language, 5th Edition

• From Middle English quaternioun, from Late Latin quaterniō, from quaternÄ« (ablative form of quater, “four times") + -iōn, “-ion".