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

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

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

In particular he explained the principle of least action, first advanced by P. L. M. de Maupertuis, and developed by Sir W. R. Hamilton, of quaternion fame.

From Encyclopaedia Britannica, 11th Edition, Volume 13, Slice 2 "Hearing" to "Helmond" by Various