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.

---

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

---

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.

---

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

See Examples For:

quaternion

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)

The play of chances which brings up a ternion or a quaternion is nothing compared to what has been required to prevent the combination of which I am reaping the fruits from being disturbed.

From Recollections of My Youth by Renan, Ernest

The customary quire is a gathering of eight leaves, forming a quaternion proper.

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)