For a simple finite-dimensional example, consider n-dimensional Euclidean space R with its usual dot product.

The real coordinate space R is the prototypical n-manifold.

The probability of finding the particle in some region of space R is given by the integral over that region:

In two-dimensional space R linear maps are described by 2 x 2 real matrices.

The complexification of real coordinate space R is complex coordinate space C.

Manifolds are often defined as embedded submanifolds of Euclidean space R, so this forms a very important special case.

For example, n-dimensional real space R can be ordered by comparing its vectors componentwise.

For every integer n, the flat space R admits an almost complex structure.

As a consequence, a perfect tiling of the Euclidean space R is impossible with regular tetrahedra.

The space R consists of all n-tuples of real numbers (x,.