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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.
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A set of four persons or items.
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(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.
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A set of four.
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(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.
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A group or set of four people or things.
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A word of four syllables.
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(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.
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Other Word Forms

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".

    From Wiktionary

Quaternion Sentence Examples

  • Thus every quaternion may be written in the form q = Sq+Vq, where either Sq or Vq may separately vanish; so that ordinary algebraic quantities (or scalars, as we shall call them) and pure vectors may each be regarded as special cases of quaternions.

  • The equations q'+x = q and y+q' = q are satisfied by the same quaternion, which is denoted by q - q'.

  • In the applications of the calculus the co-ordinates of a quaternion are usually assumed to be numerical; when they are complex, the quaternion is further distinguished by Hamilton as a biquaternion.

  • The outer and inner products of two extensive quantities A, B, are in many ways analogous to the quaternion symbols Vab and Sab respectively.

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