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)
|
