Quaternion Definition

kwə-tûrnē-ən
noun
A set of four.
Webster's New World
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.
American Heritage
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.
Webster's New World
Synonyms:
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Other Word Forms of Quaternion

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.

  • These may be compared and contrasted with such quaternion formulae as S(VabVcd) =SadSbc-SacSbd dSabc = aSbcd - bScda+cSadb where a, b, c, d denote arbitrary vectors.

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Words Starting With

QQUQUA

Words Ending With

NONION

Unscrambles

quaternion

Words Starting With Q and Ending With N

Starts With Q & Ends With NStarts With QU & Ends With NStarts With Q & Ends With ON

Word Length

10 Letter Words10 Letter Words Starting With Q10 Letter Words Ending With N