basis for tangent space of manifold

tangent space basis for manifold

Let be a smooth manifold, a point, and a chart such that .

We can define (build) a basis for the tangent space using the standard basis on . Define Notes:

• is the standard basis on , so we take the directional derivative in that direction.
• , so
• so we know how to use multivariable calculus and the total derivative.

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