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.
{|
! Notation ! Meaning
$ \mathbf{x_\textup{stuff}} $
$ x |
{|
! Notation ! Meaning
$ \hat{M} |
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:
{|
! Notation ! Meaning
$ \mathbf{x} |
$ (\mathbf{x}_\textup{stuff})^i $
I use round brackets to avoid confusion if necessary (in which case the index appears outside).
$ \tensor{T}{_i |
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.
{|
! Notation ! Meaning