Cartesian product

Bedeutung (Englisch)

1. The set of all possible ordered pairs of elements, the being first from X, the second from Y, written X×Y. Formally, the set (x,y);|;x∈X;and;y∈Y.
2. All possible combinations of rows between all of the tables listed.
3. An (m+n)-dimensional space, formally composed of all possible ordered pairs of points from X and Y, but thought of as an independent (m+n)-dimensional space (in the sense that if, e.g. X and Y are vector spaces, the elements of X×Y are thought of as (m+n)-tuples instead of ordered pairs) and written X×Y.
4. Any of several generalizations of the set-theoretic sense, especially one which shares the geometrical intuition outlined above, i.e. one such that the product can be thought of as an object in its own right and not just as a set of pairs.

Konzepte

kartesisches Produkt

Kreuzprodukt

Produktmenge

kartesianisches Produkt

Synonyme

intersection

product

product set

cross join

Übersetzungen

produit cartésien

producto cartesiano

prodotto cartesiano

produto cartesiano

تقاطُع

cartesisch product

Produto Cartesiano

kruisproduct

intersection

produit

couples

intersezione

Etymologie (Englisch)

From Cartesian + product, after French philosopher, mathematician, and scientist René Descartes (1596–1650), whose formulation of analytic geometry gave rise to the concept.