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Canonical static concept record
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An element of the tangent space at a point of a smooth manifold, equivalently a velocity of a curve or a derivation at that point.
The curve and derivation constructions are canonically equivalent for finite-dimensional smooth manifolds.
wp-tangent_vectornlab-tangent_vectorlee-smooth-manifoldsEach relation below ends at this concept.
This is an authored directed relation from the source endpoint to the target endpoint.
The derivative of a smooth curve at a parameter value defines a tangent vector.
Apply a standard functorial or canonical construction whose output is not merely a reduct of the input and is not generally an equivalent presentation of the same object.
wp-tangent_vectornlab-tangent_vectorlee-smooth-manifoldsEach relation below starts at this concept.
This is an authored directed relation from the source endpoint to the target endpoint.
Four-velocity is a normalized timelike tangent vector to a worldline.
A mathematical concept supplies part of the formal language, state space, representation, or analytic machinery used by a scientific or mathematical-physics concept. The source is the mathematical predecessor; this does not claim that physical content follows from mathematics alone.
wp-tangent_vectornlab-tangent_vectorlee-smooth-manifoldswp-physics-four_velocitynlab-physics-velocitytong-relativity