tangent space
From Mathematics wiki
The set of all tangent vectors 
at a point 
on a manifold 
forms a tangent space at , denoted by 
. The tangent space forms the dual space of the cotangent space 
. The tangent space is also a vector space.
The set of all points , and their associated tangent spaces form the tangent bundle on , denoted 
. An element of is a pair 
, where 
while 
. This is an example of a fiber bundle.
A continuous map from onto is called a tangent vector field.
back to tangent vector field
on to tangent basis
