The tangent space 
at a point 
of an 
-dimensional smooth
manifold 
is the real vector space of all manifold
tangent vectors at 
.
It has dimension 
. If 
is a smooth curve passing
through 
,
then the derivative of 
at 
is a vector in 
.
Tangent Space
See also
Chart Tangent Space, Submanifold Tangent Space, Tangent, Tangent Bundle, Tangent Plane, Tangent Vector Explore this topic in the MathWorld classroomExplore with Wolfram|Alpha
Cite this as:
Weisstein, Eric W. "Tangent Space." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/TangentSpace.html