Gaussian elimination algorithmGaussian, adj. Elimination, n. (created from a verb eliminate, /ᵻˈlɪmᵻneɪt/, and a suffix -ion) Algorithm, n. Pronounciation: /ˈɡaʊsɪən/, /ᵻˌlɪmᵻˈneɪʃn/, /ˈalɡərɪð(ə)m/ Meaning: Gaussian: Discovered or formulated by Gauss. Elimination: The removal of a constant, variable, factor, etc., from a system of equations or a matrix by algebraic manipulation. Algorithm: A procedure or set of rules used in calculation and problem-solving; (in later use spec.) a precisely defined set of mathematical or logical operations for the performance of a particular task. Source: OED |
Greatest Common Divisor (GCD) domainnoun pronunciation: [ ˈgreytist ˈkämən diˈvīzər dōˈmān ] meaning: is an integral domain with the property that any two elements have a greatest common divisor (GCD) property: If R is a GCD domain, then the polynomial ring R[X1,...,Xn] is also a GCD domain. |
Group /ɡruːp/a set of operations so constituted that the product of any number of these operations is always itself a member of the set. In later use more generally: a set of elements together with an operation for combining any two of them to form a third element which is also in the set, the operation satisfying certain conditions. Etymology: French groupe, grouppe small detachment of soldiers (1574), arrangement of two or more figures or objects in a design . 1668), (in music) series of notes forming an ornament, run, etc., or linked by a slur (1703), number of things having some related properties or attributes in common (1726) |
Group homomorphismnoun pronunciation: [ gro͞op ˌhōməˈmôrˌfizəm ] meaning: given two groups, (G, ∗) and (H, ·), a group homomorphism from (G, ∗) to (H, ·) is a function h : G → H such that for all u and v in G it holds that where the group operation on the left hand side of the equation is that of G and on the right hand side that of H. From this property, one can deduce that h maps the identity element eG of G to the identity element eH of H, and it also maps inverses to inverses in the sense that |