In mathematics, a coordinate-induced basis is a basis for the

tangent space In mathematics, the tangent space of a manifold generalizes to higher dimensions the notion of '' tangent planes'' to surfaces in three dimensions and ''tangent lines'' to curves in two dimensions. In the context of physics the tangent space to a ...

cotangent space In differential geometry, the cotangent space is a vector space associated with a point x on a smooth (or differentiable) manifold \mathcal M; one can define a cotangent space for every point on a smooth manifold. Typically, the cotangent space, T ...

of a manifold that is induced by a certain coordinate system. Given the coordinate system

x^a

, the coordinate-induced basis

e_a

of the tangent space is given by :

e_a = \frac

and the dual basis

\omega^a

of the cotangent space is :

\omega^a=dx^a. \,

References

*D.J. Hurley, M.A. Vandyck ''Topics in Differential Geometry: a New Approach Using D-Differentiation'' (2002 Springer) p. 5 Differential geometry {{differential-geometry-stub