Co-ordinate axes: What does the $e$ in ${\hat e}_x$ stand for? In vector analysis for $\mathbb{R^3}$ we write standard basis vectors in various forms like $\{\hat{x}, \hat{y}, \hat{z} \}$, $\{ \hat{\imath}, \hat{\jmath}, \hat{k}\}$, $\{ {\hat e}_x, {\hat e}_y, {\hat e}_z\}$ etc. 
What does the $e$ in the ${\hat e}_x$ stand for? My guess is it may represent that the space is euclidean.
 A: Perhaps it comes from Einheitsvektor, which means unit vector in German?
A: This applies to basis vectors in general, not only standard ones.
Think of the practice of denoting an identity element in Algebra, whatever is the algebraic structure this element happens to be in.
Usually $e$ is used, particularly when such an element is unique.
There is the uppercase variant $E$ when the structure is given on a set of linear operators of some vector space (linear operators are usually denoted by uppercase letters).
Now consider a linear operator $A\colon V\to V$ on a vector space $V$ over some field.
You can say that $A$ is known when its values $a_k$ on all basis vectors are known.
The practice of denoting the vector that the $k$-th basis vector is taken to through a linear operator by lowercasing the letter of the operator itself and subscripting it according to the basis vector is quite common.
This is even commoner when $A$ is not the operator but is its (right-multiplicative) matrix representation.
Now if one uses $E$ to denote the identity operator, it follows that $e_k$ is the vector that $k$-th basis vector is taken to by $E$, that is the $k$-th basis vector iself.
