In
mathematics, the
standard basis (also called
natural basis) for a
Euclidean space is the set of
unit vectors pointing in the direction of the axes of a
Cartesian coordinate system. For example, the standard basis for the
Euclidean plane is formed by vectors
![](http://info.babylon.com/onlinebox.cgi?rt=GetFile&uri=!!ARV6FUJ2JP&type=0&index=2126)
and the standard basis for
three-dimensional space is formed by vectors
![](http://info.babylon.com/onlinebox.cgi?rt=GetFile&uri=!!ARV6FUJ2JP&type=0&index=2774)
Here the vector
ex points in the
x direction, the vector
ey points in the
y direction, and the vector
ez points in the
z direction. There are several common
notations for these vectors, including {
ex,
ey,
ez}, {
e1,
e2,
e3}, {
i,
j,
k}, and {
x,
y,
z}. These vectors are sometimes written with a
hat to emphasize their status as unit vectors. Each of these vectors is sometimes referred to as the versor of the corresponding Cartesian axis.