Coordinate-induced basis
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In mathematics, a coordinate-induced basis is a basis for the tangent space or cotangent space of a manifold that is induced by a certain coordinate system. Given the coordinate system [math]\displaystyle{ x^a }[/math], the coordinate-induced basis [math]\displaystyle{ e_a }[/math] of the tangent space is given by
- [math]\displaystyle{ e_a = \frac{\partial}{\partial x^a} }[/math]
and the dual basis [math]\displaystyle{ \omega^a }[/math] of the cotangent space is
- [math]\displaystyle{ \omega^a=dx^a. \, }[/math]
References
- D.J. Hurley, M.A. Vandyck Topics in Differential Geometry: a New Approach Using D-Differentiation (2002 Springer) p. 5
![]() | Original source: https://en.wikipedia.org/wiki/Coordinate-induced basis.
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