- #1
demonelite123
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I sometimes see that the basis vectors of the tangent space of a manifold sometimes denoted as ∂/∂x_i which is the ith basis vector. what i am a little confused about is why is the basis vectors in the tangent space given that notation? is there a specific reason for it?
for example, i know that the basis vectors of the cotangent space of a manifold are denoted by dx_i which can be interpreted as the exterior derivative of the coordinate function f(x1,...,x_n) = x_i. is there something similar that allows one to make sense of the notation ∂/∂x_i?
Thanks.
for example, i know that the basis vectors of the cotangent space of a manifold are denoted by dx_i which can be interpreted as the exterior derivative of the coordinate function f(x1,...,x_n) = x_i. is there something similar that allows one to make sense of the notation ∂/∂x_i?
Thanks.