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WordNet
cartesian product

n. the set of elements common to two or more sets; "the set of red hats is the intersection of the set of hats and the set of red things" [syn: intersection, product]

Wikipedia
Cartesian product

In mathematics, a Cartesian product is a mathematical operation which returns a set (or product set or simply product) from multiple sets. That is, for sets A and B, the Cartesian product is the set of all ordered pairs where and . Products can be specified using set-builder notation, e.g.


A × B = { (a, b) ∣ a ∈ A and b ∈ B }.

A table can be created by taking the Cartesian product of a set of rows and a set of columns. If the Cartesian product is taken, the cells of the table contain ordered pairs of the form .

More generally, a Cartesian product of n sets, also known as an n-fold Cartesian product, can be represented by an array of n dimensions, where each element is an n- tuple. An ordered pair is a 2-tuple or couple.

The Cartesian product is named after René Descartes, whose formulation of analytic geometry gave rise to the concept, which is further generalized in terms of direct product.

Usage examples of "cartesian product".

If we split spacetime into a Cartesian product of four-dimensional Minkowski spacetime and a six-dimensional compact Kä.