Cartesian product


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cartesian product

[kär′tē·zhan ′präd·əkt]
(mathematics)
In reference to the product of P and Q, the set P × Q of all pairs (p,q), where p belongs to P and q belongs to Q.

Cartesian product

(mathematics)
(After Renee Descartes, French philosper and mathematician) The Cartesian product of two sets A and B is the set

A x B = a, b) | a in A, b in .

I.e. the product set contains all possible combinations of one element from each set. The idea can be extended to products of any number of sets.

If we consider the elements in sets A and B as points along perpendicular axes in a two-dimensional space then the elements of the product are the "Cartesian coordinates" of points in that space.

See also tuple.
References in periodicals archive ?
Thus, it is possible to conclude that the effect of distributing the databases is relatively minor to the effect of parallelizing the algorithm in computation intensive tasks such as the Cartesian Product computation.
Then the Cartesian product of r and s induced by [dot in circle] is defined as r X s {[t.
If m = 2 then this Cartesian product does not have the extendability property (except if q = 4) because of Theorem 1.
construction notation B = [empty set] Disjoint union A + B A Cartesian product A x b [empty set] Sequence SEQ (B) [epsilon] Sequence of card k > 0 [SEQ.
They are used in the following section where we completely describe graphs for which their Cartesian product with [K.
In this paper, we study the 3-connectivity of Cartesian product graphs and get the following result.
The domination related questions on the Cartesian product seems to be the most problematic among the standard products.
The next three results will determine exactly when the cartesian product of two arbitrary codes in two Hamming graphs is completely regular.
In this paper, we have discussed a subclass of interval valued neutrosophic graph called strong interval valued neutrosophic graph, and we have introduced some operations, such as Cartesian product, composition and join of two strong interval valued neutrosophic graph, with proofs.
The Cartesian product of G and H is a graph, denoted by G [?
We first give the definition of cartesian product of fuzzy SU-ideals and cartesian product of anti fuzzy SU-ideals on SU-algebra and provide some its properties.
7 show respectively for adjacent and common vertex cases, the relative error when calculating the source integral through (9) and the observer integral by means of generalized 2D Cartesian product rules based either on the DE formula or on the Gauss-Legendre rules.