# quaternions

## quaternion

[kwuh-tur-nee-uhn]
noun
1.
a group or set of four persons or things.
2.
Bookbinding. four gathered sheets folded in two for binding together.
3.
Mathematics.
a.
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.
b.
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:
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 Dictionary, © Random House, Inc. 2014.
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Collins
World English Dictionary
 quaternion (kwəˈtɜːnɪən) —n 1. maths a generalized complex number consisting of four components, x = x0 + x1i + x2j + x3k, where x, x0…x3 are real numbers and i² = j² = k² = --1, ij = --ji = k, etc 2. another word for quaternary [C14: from Late Latin quaterniōn, from Latin quaternī four at a time]

Collins English Dictionary - Complete & Unabridged 10th Edition
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American Heritage
Science Dictionary
 quaternion   (kwə-tûr'nē-ən)  Pronunciation Key  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
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Easton
Bible Dictionary

### Quaternion definition

a band of four soldiers. Peter was committed by Herod to the custody of four quaternions, i.e., one quaternion for each watch of the night (Acts 12:4). Thus every precaution was taken against his escape from prison. Two of each quaternion were in turn stationed at the door (12:6), and to two the apostle was chained according to Roman custom.

Easton's 1897 Bible Dictionary
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