Tangent Space
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Tangent Space

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High Quality Content by WIKIPEDIA articles! In mathematics, the tangent space of a manifold is a concept which facilitates the generalization of vectors from affine spaces to general manifolds, since in the latter case one cannot simply subtract two points to obtain a vector pointing from one to the other. In differential geometry, one can attach to every point x of a differentiable manifold a tangent space, a real vector space which intuitively contains the possible "directions" in which one can tangentially pass through x. The elements of the tangent space are called tangent vectors at x. Th...