# Codimension

(diff) ← Older revision | Latest revision (diff) | Newer revision → (diff)

The codimension (or quotient or factor dimension) of a subspace of a vector space is the dimension of the quotient space ; it is denoted by , or simply by , and is equal to the dimension of the orthogonal complement of in . One has If and are two subspaces of of finite codimension, then and are also of finite codimension, and The codimension of a submanifold of a differentiable manifold is the codimension of the tangent subspace of the tangent space at . If and are finite-dimensional, then If and are differentiable manifolds, if is a submanifold of and if is a differentiable mapping transversal to , then The codimension of an algebraic subvariety (or an analytic subspace) of an algebraic variety (analytic space) is the difference How to Cite This Entry:
Codimension. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Codimension&oldid=18855
This article was adapted from an original article by V.E. GovorovA.F. Kharshiladze (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article