In "A Student's Guide to Vectors and Tensors" by Daniel Fleisch, I read that the covariant metric tensor g(adsbygoogle = window.adsbygoogle || []).push({}); _{ij}=e_{i}°e_{i}(I'm leaving out the → s above the e's) where e_{i}and e_{i}are coordinate basis vectors and ° denotes the inner product, and similarly for the contravariant metric tensor using dual base vectors. But I thought the definition of base vectors included that the inner product of two distinct ones of the same type was zero, and similarly for dual base vectors. (For example, the basis vectors of R^{n}, with the inner product = the dot product.) Where is my thinking wrong?

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# Confusion about basis vectors and matrix tensor

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