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## Main Question or Discussion Point

The wikipedia article on connection forms refers to a

The connection form article uses general notation [tex]e_\alpha[/tex] for the basis elements instead of the partial derivative notation [tex]\partial_\alpha[/tex] typically used for coordinate bases. Is it because not all bases are coordinate bases?

**local frame**. What is the relationship between local frames and coordinate bases? Are they the same thing? Is one a subset of the other?The connection form article uses general notation [tex]e_\alpha[/tex] for the basis elements instead of the partial derivative notation [tex]\partial_\alpha[/tex] typically used for coordinate bases. Is it because not all bases are coordinate bases?