Codimension

The codimension referred to in different fields of mathematics, the complement to the dimension: For example, in three-dimensional space, the sum of dimension and codimension of an object equal to 3

Definition

It is a vector space over a field and a subspace. Then the codimension of in written

Equal to the dimension of the factor space.

Properties

• It is always

• Is a complement of In, i.e., it is

• If two subspaces, so we always have

• Are subspaces, the following applies