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[kwuh-tur-nee-uh n] /kwəˈtɜr ni ən/
a group or set of four persons or things.
Bookbinding. four gathered sheets folded in two for binding together.
  1. an expression of the form a + bi + cj + dk, where a, b, c, and d are real numbers; i 2 = j 2 = k 2 = −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.
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 Unabridged
Based on the Random House Dictionary, © Random House, Inc. 2018.
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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 Jarl William 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.

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

    The Court of Cacus

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

  • Next, to assign the distinction between the first and the second quaternion in propositions tertii adjacentis.

    Aristotle George Grote
  • These last words are incorrect in fact, for οὐκ ἄνθρωπος does not appear in the first quaternion, but is reserved for the second.

    Aristotle George Grote
  • Four soldiers formed a quaternion; four quaternions therefore were sixteen men, who were especially appointed to guard Peter.

    "Granny's Chapters" Lady Mary Ross
  • His days are thus described: from dawn to the third hour he copied rapidly, filling a (quaternion) each day.

  • There was no sound of trumpet at the sun's rising, but a quaternion of legionaries came and the guard was changed.

    Ulric the Jarl William O. Stoddard
British Dictionary definitions for quaternion


(maths) a generalized complex number consisting of four components, x = x0 + x1i + x2j + x3k, where x, x0x3 are real numbers and i² = j² = k² = –1, ij = –ji = k, etc
another word for quaternary (sense 5)
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
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quaternion in Science
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 © 2002. Published by Houghton Mifflin. All rights reserved.
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