Usually means: Set of all possible directions.
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We found 5 dictionaries that define the word tangent space:

General (2 matching dictionaries)
  1. tangent space: Wiktionary
  2. Tangent space: Wikipedia, the Free Encyclopedia

Computing (1 matching dictionary)
  1. tangent space: Encyclopedia

Science (2 matching dictionaries)
  1. Tangent Space: Eric Weisstein's World of Mathematics
  2. tangent space, tangent space: PlanetMath Encyclopedia

Definitions from Wiktionary (tangent space)

noun:  (topology, differential topology) An n-dimensional vector space that represents the set of all vectors tangent to given n-dimensional differentiable manifold M at point x.

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