Editing Dimension (vector space) (section)

== Examples ==

The vector space <math>\R^3</math> has
<math display=block>\left\{\begin{pmatrix} 1 \\ 0 \\ 0 \end{pmatrix}  , \begin{pmatrix} 0 \\ 1 \\ 0 \end{pmatrix} , \begin{pmatrix} 0 \\ 0 \\ 1 \end{pmatrix}\right\}</math>
as a [[standard basis]], and therefore <math>\dim_{\R}(\R^3) = 3.</math> More generally, <math>\dim_{\R}(\R^n) = n,</math> and even more generally, <math>\dim_{F}(F^n) = n</math> for any [[Field (mathematics)|field]] <math>F.</math> 

The [[complex number]]s <math>\Complex</math> are both a real and complex vector space; we have <math>\dim_{\R}(\Complex) = 2</math> and <math>\dim_{\Complex}(\Complex) = 1.</math> So the dimension depends on the base field.

The only vector space with dimension <math>0</math> is <math>\{0\},</math> the vector space consisting only of its zero element.