Notation for vector v in basis x, dimension y What is common notation for the value of the $n$th dimension of vector $v$, given by basis $x$. Is it something like $$v_{x}^{y}$$
Thanks!
 A: "The $n$th (or $y$th) dimension of vector $v$" is not a phrase I'm familiar with. As such, I assume you meant the same thing as "the $n$th component of a vector in $\mathbb R^{m}$ (or similar).
This may depend on your textbook, but as you can see in places like Change of (orthonormal) basis., one notation (which I've seen a few books use) for the $i$th component of the vector $\mathbf v$ when written in terms of an ordered basis $\mathcal B$ would be $$\left([\mathbf v]_\mathcal B\right)_i$$
If the parentheses get in your way, I imagine it would be clear (especially if you explain your notation) to write something like $[\mathbf v]^\mathcal B_i$ or perhaps even $\mathbf v^\mathcal B_i$ if you're using a convention (like I'm using \mathcal) that makes it clear at a glance that $\mathcal B$ is a basis. 
However, I would not suggest putting the index on top and the basis on the bottom unless you'd already been following a convention where the indices go on top. And I would strongly suggest not using $y$ (or $x$) for an index and not using adjacent letters in the alphabet in the same typeface to refer to an index and a basis.
