Einstein notation - difference between vectors and scalars From Wikipedia:

First, we can use Einstein notation in
  linear algebra to distinguish easily
  between vectors and covectors: upper
  indices are used to label components 
  (coordinates) of vectors, while lower
  indices are used to label components
  of covectors. However, vectors
  themselves (not their components) have
  lower indices, and covectors have
  upper indices.

I am trying to read the Wikipedia article, but I am constantly getting confused between what represents a vector/covector and what represents a component of one of these. How can I tell?

A vector component is always written with 1 upper index $a^i$, while a covector component is written with 1 lower index $a_i$.
In Einstein notation, if the same index variable appear in both upper and lower positions, an implicit summation is applied, i.e.
$$ a_i b^i = a_1 b^1 + a_2 b^2 + \dotsb \qquad (*) $$
Now, a vector is constructed from its component as
$$ \mathbf a = a^1 \mathbf{\hat e}_1 + a^2 \mathbf{\hat e}_2 + \dotsb $$
where $\mathbf{\hat e}_i$ are the basis vectors. But this takes the form like (*), so if we make basis vectors to take lower indices, we will get
$$ \mathbf a = a^i \mathbf{\hat e}_i $$
This is likely what Wikipedia means.
