Is there a symbol for the number of dimensions in a vector? Here's an equation from a text book for computing a unit vector:
$$\hat v = \frac{\overline v}{ \sqrt{ \sum ^n _{i=1}  (\overline v_i)^2 } }$$
Now I may be wrong here, but using $n$ doesn't really cut it here for me. $n$ can't be any old amount, it has to be the number of dimensions in $ \overline v$, right? So is there a symbol for the number of dimensions in a vector?
 A: Implicit in the question is that the vectors are in $\mathbb{C}^n$, which is a particular type of vector space.  There are many others, e.g. various types of function space, polynomial space, matrix space.  None of these have "coordinates" as such in their representations -- this exists only in coordinate spaces such as $\mathbb{R}^n$ or $\mathbb{C}^n$.  However to have a coordinate space you must specify how many coordinates there are; hence the notation requested is superfluous.  
Note: obviously some authors omit specifying what the ambient space is such as apparently the author of the text in question; however using the letter $n$ for the dimension of the coordinate space is so common as to be considered standard.
A: Notation typically identifies a space's dimension, not a vector's space's dimension; we write $\dim V$, not $\dim\operatorname{Space}v$ or anything like that. If $n$'s inclusion here bothers you, I recommend rewriting the sum, e.g. as $v^\ast\cdot v$ or $\sum_i\overline{v}_i^2$. (Without explicit constraints on $i$, $\sum_i$ means "sum over all relevant $i$", for a suitable definition of relevance that's obvious in context).
