Vielbeins: Is $$e^1.e^1$$ a Basis Like $$i.i=1$$?

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If $$e^1$$ is a form like the ones in tetrad formalism (vielbeins). If we have $$e^1 . e^1$$ can we treat those as basis like $$i.i=1$$?
 
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I think the reason you haven't gotten any answers is that the question is unclear.
 
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