Every textbook, website, professor, etc. uses their own notation and conventions. To avoid confusion I thought I'd write down mine and try to use them consistently throughout the site.

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! Notation ! Meaning

$ \mathbf{x_\textup{stuff}} $

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! Notation ! Meaning

Generally I avoid using indices because of the inherent complexity associated with coordinates. When I do, though, I try to be consistent with Ricci calculus. Below is a quick summary:

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! Notation ! Meaning

$ (\mathbf{x}_\textup{stuff})^i $

I use round brackets to avoid confusion if necessary (in which case the index appears outside).

When the tensor is treated as a linear transformation, this is the element of the corresponding matrix that lies at the intersection of the i-th row and the j-th column.
If $i$ and $j$ are undefined then this denotes the entire tensor.

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! Notation ! Meaning