A standard basis, also called a natural basis, is a special orthonormal vector basis in which each basis vector has a single nonzero entry with value 1. In 
-dimensional Euclidean space 
, the vectors are usually denoted 
(or 
) with 
, ..., 
, where 
is the dimension of the vector space that is spanned by this basis according to
 | (1) |
For example, in the Euclidean plane 
, the standard basis is
 |  |  | (2) |
 |  |  | (3) |
Similarly, for Euclidean 3-space 
, the standard basis is
 |  |  | (4) |
 |  |  | (5) |
 |  |  | (6) |
