# quaternion

[ kwuh-tur-nee-uh n ]

/ kwəˈtɜr ni ən /

### noun

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.

## RELATED WORDS

tetralogy, tetrad, quaternity, quadrivium, quadruplet, quadruple, quaternary, quadrumvirate, quartet, quadrigeminal

## Nearby words

- quatercentennial,
- quaternary,
- quaternary ammonium compound,
- quaternary structure,
- quaternate,
- quaternity,
- quathlamba,
- quatorze,
- quatrain,
- quatre

## 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

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Based on the Random House Unabridged Dictionary, © Random House, Inc. 2019

## Examples from the Web for quaternion

## quaternion

/ (kwəˈtɜːnɪən) /

### noun

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)

## Word Origin for quaternion

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.

The American Heritage® Science Dictionary
Copyright © 2011. Published by Houghton Mifflin Harcourt Publishing Company. All rights reserved.