Editing Codimension (section)

{{short description|Difference between the dimensions of mathematical object and a sub-object}}
In [[mathematics]], '''codimension''' is a basic [[Geometry|geometric]] idea that applies to [[vector subspace|subspaces]] in [[vector space]]s, to [[submanifold]]s in [[manifold]]s, and suitable [[subset]]s of [[algebraic varieties]].

For [[affine variety|affine]] and [[projective algebraic varieties]], the codimension equals the [[height (ring theory)|height]] of the defining [[ideal (ring theory)|ideal]]. For this reason, the height of an ideal is often called its codimension.

The dual concept is [[relative dimension]].