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 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.
Other names for the direct product that have appeared in the literature are tensor product, Kronecker product, cardinal product, relational product, cross product, conjunction, weak direct product, Cartesian product, product, or categorical product.
The Cartesian product [mu] x [beta] : X x X [right arrow] [0, 1] is define by ([mu] x [beta])(x, y) = min{[mu](x), [beta](y)} for all x, y [member of] X.
This section is devoted to show the worthiness of using 2D Cartesian product rules based on DE formula to integrate potentials as (9) to compute the Galerkin-MoM matrix static interactions within a SIE-MoM framework.
The difference is that the complex pattern is a Cartesian product of three sets instead of two, which can be formalized as: R [subset or equal to] X x Y x Z.
n] is defined as a subset of the Cartesian product [A.
Thus a relation is a subset of a Cartesian product of sets (value domains).
For students who have taken introductory courses in graph theory and algebra, Imrich (Montanuniversitat Leoben, Austria) and other experts in the field introduce the Cartesian product (the product set containing all possible combinations of one element from each set).
Another possible extension is to functions bandlimited to the Cartesian product of two (or more) balls.
Each tuple in the result of a cartesian product reflects the conjunction of two events.