quaternion

qua·ter·ni·on

Q0021700 (kwə-tûr′nē-ən)n.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 k^wetwer- in Indo-European roots.]

quaternion

(kwəˈtɜːnɪən) n1. (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, etc2. another word for quaternary⁵[C14: from Late Latin quaterniōn, from Latin quaternī four at a time]

qua•ter•ni•on

(kwəˈtɜr ni ən)

n. 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]

Thesaurus

Noun

quaternion - the cardinal number that is the sum of three and oneIV, Little Joe, quadruplet, quartet, quatern, 4, four, quaternity, tetrad, foursome, quaternarydigit, figure - one of the elements that collectively form a system of numeration; "0 and 1 are digits"

Translations

кватернион

quaternion

(kwətûr`nēən), in mathematics, a type of higher complex number first suggested by Sir William R. Hamilton in 1843. A complex number is a number of the form a+bi when a and b are real numbers and i is the so-called imaginary unit defined by the equation i²=−1. The rules for operating with complex numbers are simply those of operating with the polynomial a+bx except that i² is replaced by −1 whenever it occurs. A quaternion, an extension of this concept, is a number of the form a+bi+cj+dk when a, b, c, and d are real numbers and i, j, and k are imaginary units defined by the equations i²=j²=k²=ijk=−1. Quaternions, as well as vectorsvector,
quantity having both magnitude and direction; it may be represented by a directed line segment. Many physical quantities are vectors, e.g., force, velocity, and momentum.
..... Click the link for more information. and tensorstensor,
in mathematics, quantity that depends linearly on several vector variables and that varies covariantly with respect to some variables and contravariantly with respect to others when the coordinate axes are rotated (see Cartesian coordinates).
..... Click the link for more information. (later outgrowths of the concept of quaternions), have many important applications in mechanics.

quaternion

[kwə′ter·nē·ən] (mathematics) The division algebra over the real numbers generated by elements i, j, k subject to the relations i ²= j ²= k ²= -1 and ij = -ji = k, jk = -kj = i, and ki = -ik = j. Also known as hypercomplex number.

quaternion

qua·ter·ni·on

quaternion

qua•ter•ni•on

quaternion

quaternion

quaternion

quaternion

Synonyms for quaternion

noun the cardinal number that is the sum of three and one

Synonyms

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