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 {\displaystyle x^{a}} , the coordinate-induced basis e a {\displaystyle e_{a}} of the tangent space is given by e a = ∂ ∂ x a {\displaystyle e_{a}={\frac {\partial }{\partial x^{a}}}} and the dual basis ω a {\displaystyle \omega ^{a}} of the cotangent space is ω a = d x a .
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 {\displaystyle x^{a}} , the coordinate-induced basis e a {\displaystyle e_{a}} of the tangent space is given by e a = ∂ ∂ x a {\displaystyle e_{a}={\frac {\partial }{\partial x^{a}}}} and the dual basis ω a {\displaystyle \omega ^{a}} of the cotangent space is ω a = d x a .
Source: Wikipedia "Coordinate-induced basis" · CC BY-SA 4.0
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