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isometric embedding

См. также в других словарях:

  • Embedding — In mathematics, an embedding (or imbedding) is one instance of some mathematical structure contained within another instance, such as a group that is a subgroup.When some object X is said to be embedded in another object Y , the embedding is… …   Wikipedia

  • Nash embedding theorem — The Nash embedding theorems (or imbedding theorems), named after John Forbes Nash, state that every Riemannian manifold can be isometrically embedded into some Euclidean space. Isometric means preserving the length of every path. For instance,… …   Wikipedia

  • Differential geometry of surfaces — Carl Friedrich Gauss in 1828 In mathematics, the differential geometry of surfaces deals with smooth surfaces with various additional structures, most often, a Riemannian metric. Surfaces have been extensively studied from various perspectives:… …   Wikipedia

  • Nonlinear dimensionality reduction — High dimensional data, meaning data that requires more than two or three dimensions to represent, can be difficult to interpret. One approach to simplification is to assume that the data of interest lies on an embedded non linear manifold within… …   Wikipedia

  • Metric space aimed at its subspace — In mathematics, a metric space aimed at its subspace is a categorical construction that has a direct geometric meaning. It is also a useful step toward the construction of the metric envelope, or tight span, which are basic (injective) objects of …   Wikipedia

  • Einbettungssatz von Nash — Der Einbettungssatz von Nash (nach John Forbes Nash Jr.) ist ein Ergebnis aus dem mathematischen Teilgebiet der riemannschen Geometrie. Er besagt, dass jede riemannsche Mannigfaltigkeit isometrisch in einen euklidischen Raum für ein geeignetes n… …   Deutsch Wikipedia

  • Tight span — If a set of points in the plane, with the Manhattan metric, has a connected orthogonal convex hull, then that hull coincides with the tight span of the points. In metric geometry, the metric envelope or tight span of a metric space M is an… …   Wikipedia

  • Anti de Sitter space — In mathematics and physics, n dimensional anti de Sitter space, sometimes written AdS n, is a maximally symmetric Lorentzian manifold with constant negative scalar curvature. It is the Lorentzian analog of n dimensional hyperbolic space, just as… …   Wikipedia

  • Median graph — The median of three vertices in a median graph In mathematics, and more specifically graph theory, a median graph is an undirected graph in which any three vertices a, b, and c have a unique median: a vertex m(a,b,c) that belongs to shortest… …   Wikipedia

  • Gromov–Hausdorff convergence — Gromov–Hausdorff convergence, named after Mikhail Gromov and Felix Hausdorff, is a notion for convergence of metric spaces which is a generalization of Hausdorff convergence. Gromov–Hausdorff distanceGromov–Hausdorff distance measures how far two …   Wikipedia

  • Rado graph — The Rado graph, as numbered by Rado (1964). In the mathematical field of graph theory, the Rado graph, also known as the random graph or the Erdős–Renyi graph, is the unique (up to isomorphism) countable graph R such that for any finite graph G… …   Wikipedia

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