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linear submanifold

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  • Submanifold — In mathematics, a submanifold of a manifold M is a subset S which itself has the structure of a manifold, and for which the inclusion map S rarr; M satisfies certain properties. There are different types of submanifolds depending on exactly which …   Wikipedia

  • Correlation — In probability theory and statistics, correlation, (often measured as a correlation coefficient), indicates the strength and direction of a linear relationship between two random variables. In general statistical usage, correlation or co relation …   Wikipedia

  • Projection-slice theorem — In mathematics, the projection slice theorem in two dimensionsstates that the Fourier transform of the projectionof a two dimensional function f (r) onto a lineis equal to a slice through the origin of the two dimensional Fourier transform of… …   Wikipedia

  • Codimension — In mathematics, codimension is a basic geometric idea that applies to subspaces in vector spaces, and also to submanifolds in manifolds, and suitable subsets of algebraic varieties. The dual concept is relative dimension. Contents 1 Definition 2… …   Wikipedia

  • Symplectic manifold — In mathematics, a symplectic manifold is a smooth manifold, M, equipped with a closed nondegenerate differential 2 form, ω, called the symplectic form. The study of symplectic manifolds is called symplectic geometry or symplectic topology.… …   Wikipedia

  • First class constraint — In Hamiltonian mechanics, consider a symplectic manifold M with a smooth Hamiltonian over it (for field theories, M would be infinite dimensional). Poisson bracketsSuppose we have some constraints : f i(x)=0, for n smooth functions :{ f i } {i=… …   Wikipedia

  • Moving frame — The Frenet Serret frame on a curve is the simplest example of a moving frame. In mathematics, a moving frame is a flexible generalization of the notion of an ordered basis of a vector space often used to study the extrinsic differential geometry… …   Wikipedia

  • Metric tensor — In the mathematical field of differential geometry, a metric tensor is a type of function defined on a manifold (such as a surface in space) which takes as input a pair of tangent vectors v and w and produces a real number (scalar) g(v,w) in a… …   Wikipedia

  • Current (mathematics) — In mathematics, more particularly in functional analysis, differential topology, and geometric measure theory, a k current in the sense of Georges de Rham is a functional on the space of compactly supported differential k forms, on a smooth… …   Wikipedia

  • Frobenius theorem (differential topology) — In mathematics, Frobenius theorem gives necessary and sufficient conditions for finding a maximal set of independent solutions of an overdetermined system of first order homogeneous linear partial differential equations. In modern geometric terms …   Wikipedia

  • Glossary of differential geometry and topology — This is a glossary of terms specific to differential geometry and differential topology. The following two glossaries are closely related: *Glossary of general topology *Glossary of Riemannian and metric geometry.See also: *List of differential… …   Wikipedia

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