Tangent Vectors as Derivations

Statements

Theorem. The mapping between the Euclidean Tangent Space at $p$ and the set of all derivations at $p$, i.e., the vector-valued function defined as

\phi:&T_p(\mathbb{R}^n)&\to&\mathcal{D}_p(\mathbb{R}^n)\\ &v&\mapsto&D_v=D(p)v \end{array}$$ is an [[isomorphism]] between vector spaces. ## References [[Tu, L. W. - An introduction to manifolds|@Tu11 Section 2.3]]