Coordinate-induced basis explained

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

x ^{a} , the coordinate-induced basis e _{a} of the tangent space is given by e _{a} = (\partial)/(\partial x ^{a}) 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