quaternion

American  

[kwuh-tur-nee-uhn] / kwəˈtɜr ni ən /

noun

1. a group or set of four persons or things.

2. Bookbinding. four gathered sheets folded in two for binding together.

3. Mathematics.

   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.

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quaternion British  

/ kwəˈtɜːnɪən /

noun

1. 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

2. another word for quaternary

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quaternion Scientific  

/ kwə-tûr′nē-ən /

1. Any number of the form a + bi + cj + dk where a, b, c, and d are real numbers, ij = k, i ² = j ² = −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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Etymology

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

Example Sentences

Indeed, mere months after Hamilton’s quaternion brain wave, his friend John T. Graves debuted “octaves,” a kind of double quaternion now called octonions.

From Slate • Oct. 14, 2016

If you derive a quaternion multiplication table from the fundamental formula Hamilton carved into Broome Bridge, you’ll find that ij = k, but ji = -k.

From Slate • Oct. 14, 2016

It would be natural, therefore, to suppose that our fragment did not constitute a complete gathering in itself but formed part of a quaternion.

From A Sixth-Century Fragment of the Letters of Pliny the Younger A Study of Six Leaves of an Uncial Manuscript Preserved in the Pierpont Morgan Library New York by Lowe, E. A. (Elias Avery)

A quaternion of pieces called “The Nights” will supply us perhaps with our best single extract, at once practicable and characteristic.

From French Classics by Wilkinson, William Cleaver

Outside the quaternion were the dancing Pauppukkeewis, the Whirlwind, and the fierce and shifty hero, Monobozho, the North-West Wind.

From Nature Mysticism by Mercer, John Edward