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1. A set of four persons or items.
2. Mathematics 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 multiplication is not commutative.

[Middle English quaternioun, from Late Latin quaterniō, quaterniōn-, from Latin quaternī, by fours, from quater, four times; see kwetwer- in the Appendix of Indo-European roots.]


1. (Mathematics) 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 quaternary5
[C14: from Late Latin quaterniōn, from Latin quaternī four at a time]


(kwəˈtɜr ni ən)

1. a group or set of four persons or things.
2. a generalization of a complex number to four dimensions with three different imaginary units in which a number is represented as the sum of a real scalar and three real numbers multiplying each of the three imaginary units.
[1350–1400; Middle English quaternioun < Late Latin quaterniō= Latin quatern(ī) four at a time + -iō -ion]
ThesaurusAntonymsRelated WordsSynonymsLegend:
Noun1.quaternion - the cardinal number that is the sum of three and onequaternion - the cardinal number that is the sum of three and one
digit, figure - one of the elements that collectively form a system of numeration; "0 and 1 are digits"
References in classic literature ?
Aire, and ye Elements the eldest birth Of Natures Womb, that in quaternion run Perpetual Circle, multiform; and mix And nourish all things, let your ceasless change Varie to our great Maker still new praise.
I surmise that two quaternions were missing, and one of them is ours, Garrett 196B, fols.
involving LH doublets and RH singlets, is dictated by the mathematics of quaternions acting on quaternions, verified by the empirically determined maximum parity violation.
40 lifts columns (in the configuration of quaternions in modularly configurable sextuplets) inclusive of related control units, necessary for the maintenance needs of remittances ATAC buses inside surface.
The inclusion of the SDK enables developers to directly access the raw data and quaternions of the headtracker, which then can be used for programming.
cross product] is the quaternions product and-the quaternion conjugate (Dumas et al.
There are techniques that parameterize rotation with the help of quaternions (6), (7); others use an axis and angle representation (8).
Glossing quaternions as an algebra of four dimensions, consisting of the three of space and the fourth of time, he goes on to declare that he formulated his best account of them in his 1846 poem "The Tetractys":
When reading, the man troubled by acedia yawns a lot, and easily falls asleep, rubs his face, and extends his hands, and, moving the eyes away from the book, examines the wall, turning back again, he reads a little, and wastes his time turning over the pages in order to see where the text ends, counts the leaves, and calculates the number of the quaternions, finds fault with the hand-writing and the ornamentation, finally, having closed the book, puts his head on it and sleeps quite a superficial sleep, in fact then the hunger awakes his soul, and he takes care of his business.
Direct product construction also generates complex numbers, quaternions, Pauli spin matrices, and Dirac gamma matrices.
Quaternions were invented by Sir William Rowan Hamilton as an extension to the complex numbers.