Dictionary

Cartesian product

Noun

Cartesian product (plural Cartesian products)

(set theory) The set of all possible pairs of elements whose components are members of two sets. Notation: X \times Y = \{(x,y)\|x\in X \land y\in Y\}.
(databases) All possible combinations of rows between all of the tables listed.
(geometry) The set of points in an (m + n)-dimensional Cartesian space corresponding to all possible pairs of points from the two sets from spaces of dimension m and n. Notation: X \times Y = \{ (x_1, ... x_m, y_1, ... y_n) \| (x_1, ... x_m)\in X \land (y_1, ... y_n)\in Y \}.
- 1987, M. Göckeler, T. Schücker, Differential Geometry, Gauge Theories, and Gravity, 1989, page 98 ↗,
  On the Cartesian product of two manifolds a differentiable structure can be constructed in the following way.
- 1997, Michel Marie Deza, Monique Laurent, Geometry of Cuts and Metrics, 2009, page 297 ↗,
  The hypercube is the simplest example of a Cartesian product of graphs; indeed, the m-hypercube is nothing but (K₂)^m.
- 2004, David Bao, Colleen Robles, Ricci and Flag Curvatures in Finsler Geometry, David Dai-Wai Bao, Robert L. Bryant, Shiing-Shen Chern, Zhomgmin Shen (editors), A Sampler of Riemann-Finsler Geometry, page 246 ↗,
  A moment's thought convinces us of the following:
  The Cartesian product of two Riemannian Einstein metrics with the same constant Ricci scalar ρ is again Ricci-constant, and has Ric = ρ.

Synonyms

Translations

This text is extracted from the Wiktionary and it is available under the CC BY-SA 3.0 license | Terms and conditions | Privacy policy 0.004