Definition:Codimension of Vector Subspace

Definition

Let $V$ be a vector space over a field $K$.

Let $W \subseteq V$ be a subspace.

Then the codimension of $W$ in $V$ is defined as:

$\map {\mathrm {codim} } W := \map \dim {V / W}$

where $V / W$ is the quotient space of $V$ by $W$.

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