Subspace Codimensions

Definition

Suppose $W$ is a subspace of a vector space $V$. The codimension of $W$ in $V$ is the difference of the dimension of $V$ and the dimension of $W$. In this context, $V$ is called the ambient space of $W$.

Notation

As usual, let $\dim W$ and $\dim V$ denote the dimensions of $W$ and $V$, respectively We denote the codomension of $W$ in $V$ by $\codim(W)$