Cartesian product

English Alternative forms en cartesian product Etymology From en Cartesian + en product, after French philosopher, mathematician, and scientist René Descartes (1596–1650), whose formulation of analytic geometry gave rise to the concept. Noun en set theory of two sets and The set of all possible ordered pairs of elements, the being first from , the second from , written . Formally, the set . en databases All possible combinations of rows between all of the tables listed. en geometry of an m-dimensional space and an n-dimensional space An (m+n)-dimensional space, formally composed of all possible ordered pairs of points from and , but thought of as an independent (m+n)-dimensional space (in the sense that if, e.g. and are vector spaces, the elements of are thought of as (m+n)-tuples instead of ordered pairs) and written . en 1987 M. Göckeler; T. Schücker Differential Geometry, Gauge Theories, and Gravity https://books.google.com.au/books?id=Lr8zo2caBWYC&pg=PA98&dq=%22cartesian+product%22%7C%22cartesian+products%22+geometry&hl=en&sa=X&ved=0ahUKEwjAk4Kkp67NAhWIXaYKHbJVBBQQ6AEIRjAH#v=onepage&q=%22cartesian%20product%22%7C%22cartesian%20products%22%20geometry&f=false 98 1989 On the Cartesian product of two manifolds a differentiable structure can be constructed in the following way. en mathematics 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. en 1997 Michel Marie Deza; Monique Laurent Geometry of Cuts and Metrics https://books.google.com.au/books?id=XujvCAAAQBAJ&pg=PA297&dq=%22cartesian+product%22%7C%22cartesian+products%22+geometry&hl=en&sa=X&ved=0ahUKEwjAk4Kkp67NAhWIXaYKHbJVBBQQ6AEIHTAA#v=onepage&q=%22cartesian%20product%22%7C%22cartesian%20products%22%20geometry&f=false 297 2009 The hypercube is the simplest example of a Cartesian product of graphs; indeed, the m-hypercube is nothing but (K2)m. en 2004 David Bao; Colleen Robles Ricci and Flag Curvatures in Finsler Geometry David Dai-Wai Bao; Robert L. Bryant; Shiing-Shen Chern; Zhomgmin Shen A Sampler of Riemann-Finsler Geometry https://books.google.com.au/books?id=KMZl_iQR5IUC&pg=PA246&dq=%22cartesian+product%22%7C%22cartesian+products%22+geometry&hl=en&sa=X&ved=0ahUKEwjAk4Kkp67NAhWIXaYKHbJVBBQQ6AEITTAI#v=onepage&q=%22cartesian%20product%22%7C%22cartesian%20products%22%20geometry&f=false 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 set of possible pairs en direct product Translations set of possible pairs Chinese: Mandarin: cmn 笛卡兒積 Díkǎ'ér jī, cmn 笛卡爾乘積 Díkǎ'ěr chéngjī Czech: cs kartézský součin m Dutch: nl cartesisch product n, nl kruisproduct n Estonian: et Cartesiuse korrutis, et otsekorrutis, et ristikorrutis Finnish: fi karteesinen tulo, fi tulojoukko French: fr produit cartésien m German: de kartesisches Produkt n, de Kreuzprodukt n Greek: el καρτεσιανό γινόμενο n Italian: it prodotto cartesiano m Japanese: ja デカルト積 Dekaruto seki, ja 直積集合 ちょくせきしゅうごう, chokuseki shūgō direct product Māori: mi whātuinga takirua Polish: pl iloczyn kartezjański m, pl produkt kartezjański m Portuguese: pt produto cartesiano m Romanian: ro produs cartezian n Russian: ru дека́ртово произведе́ние n dɛkártovo proizvedénije, ru прямо́е произведе́ние n direct product Serbo-Croatian: sh Kartezijev produkt m Spanish: es producto cartesiano m en eponyms