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I just wanted to make sure it was correct.

[itex]g^{\alpha\beta}[/itex] =[itex]\widehat{e}^{i}\ast \widehat{e}^{j}[/itex]

Which says that the dot product of two unit vectors equals the metric tensor. Like I said, I am very new to this stuff and I'm just trying to get the hang of it.