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rank of differential

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  • Rank — is a very broad term with several meanings. As a noun it is usually related to a relative position or to some kind of ordering (see also ranking). As an adjective it is used to mean profuse, conspicuous, absolute, or unpleasant, especially in… …   Wikipedia

  • Rank (mathematics) — Rank means a wide variety of things in mathematics, including: * Rank (linear algebra) * Rank of a tensor * Rank of an abelian group * Rank of a Lie group * Percentile rank * Rank (differential topology) * Rank of a vector bundle * Rank (set… …   Wikipedia

  • Differential centrifugation — is a common procedure in microbiology and cytology used to separate certain organelles from whole cells for further analysis of specific parts of cells. In the process, a tissue sample is first homogenised to break the cell membranes and mix up… …   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

  • Rank (differential topology) — In mathematics, the rank of a differentiable map f : M → N between differentiable manifolds at a point p ∈ M is the rank of the derivative of f at p. Recall that the derivative of f at p is a linear map from the tangent space at p to the… …   Wikipedia

  • Differential form — In the mathematical fields of differential geometry and tensor calculus, differential forms are an approach to multivariable calculus that is independent of coordinates. Differential forms provide a better[further explanation needed] definition… …   Wikipedia

  • Differential topology — In mathematics, differential topology is the field dealing with differentiable functions on differentiable manifolds. It is closely related to differential geometry and together they make up the geometric theory of differentiable manifolds.… …   Wikipedia

  • Rank (linear algebra) — The column rank of a matrix A is the maximum number of linearly independent column vectors of A. The row rank of a matrix A is the maximum number of linearly independent row vectors of A. Equivalently, the column rank of A is the dimension of the …   Wikipedia

  • Rank–nullity theorem — In mathematics, the rank–nullity theorem of linear algebra, in its simplest form, states that the rank and the nullity of a matrix add up to the number of columns of the matrix. Specifically, if A is an m by n matrix over the field F , then :rank …   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

  • Pullback (differential geometry) — Suppose that φ : M → N is a smooth map between smooth manifolds M and N ; then there is an associated linear map from the space of 1 forms on N (the linear space of sections of the cotangent bundle) to the space of 1 forms on M . This linear map… …   Wikipedia

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