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 ?
The Cartesian product of the non-regular harmonic graphs is not a harmonic graph.
Hence the Cartesian product of non-regular harmonic graphs is not a harmonic graph.
Graphical to textual conversion of specializations and Cartesian products Specialization Cartesian product CompositeProcess(Process) OutReferred [subset or equal to] Output x Artifact AtomicProcess(Proceu) InReferred [subset or equal to] Input x Artifact PostCondition(Condition) PreCondition(Condition) Table 4.
Table 3 shows the specialization relations and Cartesian products as a result of converting the related visual formalisms found in figure 2.
The measure of similarity corresponding to the Cartesian product
bar] of the Cartesian product USERS can be defined in accordance with theorem 2:
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.
The product of a matrix by a vector or by a matrix is obtained by the classical formulas in sums of products forms, sums being interpreted as disjoint unions and products as cartesian products, themselves obtained by grafting at a bud following Eq.
Fourier transforms that vanish outside ellipsoids and outside Cartesian products of balls are also considered.
Cartesian products are added as the left child of its parent.
This is done by maximizing the number of cartesian products and joins with two operators as children.
As observed in previous works, there is a trade-off between the communication and the efficiency of a parallel Join algorithm, as the whole Cartesian Product can be computed in one machine without any communication overhead.