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.
  1. 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.
  2. 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.

Nearby words

  1. quatercentennial,
  2. quaternary,
  3. quaternary ammonium compound,
  4. quaternary structure,
  5. quaternate,
  6. quaternity,
  7. quathlamba,
  8. quatorze,
  9. quatrain,
  10. 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

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

Examples from the Web for quaternion


British Dictionary definitions 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 0x 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

Science definitions for quaternion

quaternion

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