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tangent vector
:''For a more general, but much more technical, treatment of tangent vectors, see tangent space.''
In mathematics, a tangent vector is a vector that is tangent to a curve or surface at a given point. Tangent vectors are described in the differential geometry of curves in the context of curves in R''n''. More generally, tangent vectors are elements of a tangent space of a differentiable manifold. Tangent vectors can also be described in terms of germs. In other words, a tangent vector at the point is a linear derivation of the algebra defined by the set of germs at .
== Motivation ==
Before proceeding to a general definition of the tangent vector, we discuss its use in calculus and its tensor properties.
抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』
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