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## Main Question or Discussion Point

I have been reading an introductory book to General Relativity by H Hobson. I have been following it step by step and now I am stuck. It is stated in the book that:

"It is straightforward to show that the coordinate and dual basis vectors

themselves are related...

"e

I have been trying to prove it as follows:

e

=g

(e

Because e

My question: is it a correct approach?

"It is straightforward to show that the coordinate and dual basis vectors

themselves are related...

"e

_{a}= g_{ab}e^{b}...."I have been trying to prove it as follows:

e

_{a}.e_{b}=g_{ab}=g_{af}[itex]\delta[/itex]^{f}_{b}=g

_{af}(e^{f}.e_{b})(e

_{a}-g_{af}e^{f}).e_{b}=0Because e

_{b}≠0, the other side is and hence proved the given statement.My question: is it a correct approach?