Definition
Def
Let
be a smooth manifold (a surface) inside , and let be a point on . Consider all possible smooth curves
such that . The tangent space is the set of all possible velocity vectors of these curves at :
Tangent Space [ Gradient Definition]
Let a surface be defined by the level set of a function
. The tangent space at point
is the null space (kernel) of the derivative (gradient) of at :