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. This is a generalization of the notion of a bound vector in a Euclidean space. All the tangent spaces have the same dimension, equal to the dimension of the manifold.

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