# quaternion

[kwuh-tur-nee-uh n]

- a group or set of four persons or things.
- Bookbinding. four gathered sheets folded in two for binding together.
- Mathematics.
- an expression of the form a + bi + cj + dk, where a, b, c, and d are real numbers; i2 = j2 = k2 = −1; and ij = −ji = k, jk = −kj = i, and ki = −ik = j.
- a quantity or operator expressed as the sum of a real number and three complex numbers, equivalent to the quotient of two vectors. The field of quaternions is not commutative under multiplication.

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## Origin of quaternion^{}

1350–1400; Middle English quaternioun < Late Latin quaterniōn- (stem of quaterniō), equivalent to Latin quatern(ī) four at a time + -iōn- -ion

Dictionary.com Unabridged
Based on the Random House Unabridged Dictionary, © Random House, Inc. 2018

## Examples from the Web for quaternion

### Historical Examples

#### Even then the captain of the gate was replying to a question from the quaternion.

Ulric the JarlWilliam O. Stoddard

#### Should neither player be able to form a quaternion, then the game is drawn.

#### The quaternion was a gathering of four sheets of vellum, each folded once; thus forming sixteen pages.

Illuminated Manuscripts in Classical and Mediaeval TimesJ. Henry Middleton

#### William Hare, the second of our quaternion, was also a native of Ireland, having been born in the neighbourhood of Londonderry.

The Court of CacusAlexander Leighton

#### As regard class of the first quaternion, like Sancho Panza I have no intention of indicating how old these may be.

Legends & Romances of SpainLewis Spence

# quaternion

- maths a generalized complex number consisting of four components, x = x 0 + x 1 i + x 2 j + x 3 k, where x, x 0 … x 3 are real numbers and i² = j² = k² = –1, ij = –ji = k, etc
- another word for quaternary (def. 5)

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## Word Origin

C14: from Late Latin quaterniōn, from Latin quaternī four at a time

Collins English Dictionary - Complete & Unabridged 2012 Digital Edition
© William Collins Sons & Co. Ltd. 1979, 1986 © HarperCollins
Publishers 1998, 2000, 2003, 2005, 2006, 2007, 2009, 2012

# quaternion

[kwə-tûr′nē-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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The American Heritage® Science Dictionary
Copyright © 2011. Published by Houghton Mifflin Harcourt Publishing Company. All rights reserved.