# componentwise

componentwise
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English-Russian dictionary of computer science and programming. 2013.

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• Componentwise inequality — In mathematics, a componentwise inequality is an expression of the form: [1][2][3] The vectors do not have to be real, they can be from any space in which the inequality relation is defined. See also …   Wikipedia

• Direct sum of modules — For the broader use of the term in mathematics, see Direct sum. In abstract algebra, the direct sum is a construction which combines several modules into a new, larger module. The result of the direct summation of modules is the smallest general… …   Wikipedia

• Dual quaternion — The set of dual quaternions is an algebra that can be used to represent spatial rigid body displacements.[1] A dual quaternion is an ordered pair of quaternions Â = (A, B) and therefore is constructed from eight real parameters. Because rigid… …   Wikipedia

• Dominance order — Example of dominance ordering of partitions of n. Here, n = 6, nodes are partitions of 6, edges indicate that the upper node dominates the lower node. While this particular partial ordering is graded, this is not true for the dominance ordering… …   Wikipedia

• Direct product of groups — Concepts in group theory category of groups subgroups, normal subgroups group homomorphisms, kernel, image, quotient direct product, direct sum semidirect product, wreath product …   Wikipedia

• Direct product — In mathematics, one can often define a direct product of objects already known, giving a new one. This is generally the Cartesian product of the underlying sets, together with a suitably defined structure on the product set. More abstractly, one… …   Wikipedia

• Vector space — This article is about linear (vector) spaces. For the structure in incidence geometry, see Linear space (geometry). Vector addition and scalar multiplication: a vector v (blue) is added to another vector w (red, upper illustration). Below, w is… …   Wikipedia

• Hyperreal number — *R redirects here. For R*, see Rockstar Games. The system of hyperreal numbers represents a rigorous method of treating the infinite and infinitesimal quantities. The hyperreals, or nonstandard reals, *R, are an extension of the real numbers R… …   Wikipedia

• Ordered group — In abstract algebra, an ordered group is a group (G,+) equipped with a partial order ≤ which is translation invariant ; in other words, ≤ has the property that, for all a , b , and g in G , if a ≤ b then a+g ≤ b+g and g+a ≤ g+b . Note that… …   Wikipedia

• Product (category theory) — In category theory, the product of two (or more) objects in a category is a notion designed to capture the essence behind constructions in other areas of mathematics such as the cartesian product of sets, the direct product of groups, the direct… …   Wikipedia

• Supermodular — In mathematics, a function:fcolon R^k o Ris supermodular if:f(x lor y) + f(x land y) geq f(x) + f(y)for all x , y isin R k , where x vee y denotes the componentwise maximum and x wedge y the componentwise minimum of x and y .If − f is… …   Wikipedia

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