Why are basis vectors represented with subscripts instead of superscripts? Aren’t they vectors too? Isn’t a vector a linear combination of basis vectors (and not basis co-vectors?)(adsbygoogle = window.adsbygoogle || []).push({});

In David McMahon’s Relativity Demystified, he says,

“We will often label basis vectors with the notation [itex]e_a[/itex]. Using the Einstein summation convention, a vector V can be written in terms of some basis as [itex] V=V^{a}e_{a}[/itex]. In this context the notation [itex]e_a[/itex] makes sense, because we can use it in the summation convention (this would not be possible with the cumbersome [itex] (\hat{i}, \hat{j}, \hat{k} ) [/itex] for example).”

But using the Einstein summation convention, [itex] V=V^{a}e_{a}[/itex] is the inner product of a vector and a co-vector, which is a scalar and not a vector at all.

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# I Confused about basis vector notation

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