Tangent Space (Real Vector Functions)#

Definition: Tangent Space

Let \(f: \mathcal{D} \subseteq \mathbb{R}^m\to \mathbb{R}^n\) be a real vector function which is totally differentiable at an interior point \(\boldsymbol{p}\) of \(\mathcal{D}\).

The tangent space of \(f\) at \(\boldsymbol{p}\) is the