- #1
cpsinkule
- 174
- 24
In Wald's GR he makes use of a coordinate basis consisting of ∂/∂x[itex]^{n}[/itex] where n runs over the coordinates, and I understand his argument that ∂f/∂x[itex]^{n}[/itex] are tangent vectors, but I can't wrap my head around the operator ∂/x[itex]^{n}[/itex] spanning a tangent space of a manifold. Any clarification on this would be appreciated. He also states that dx[itex]^{m}[/itex]∂/∂x[itex]^{n}[/itex]=δ[itex]^{m}[/itex][itex]_{n}[/itex], but I don't see how this is true, either. I know fully well that for them to be a basis of the dual and vector space respectively they must satisfy that condition, but I don't see how he arrives at that. Is it just by definition that dx∂/∂x=δ?