Source: cirosantilli/underlying-field-of-a-vector-space

= Underlying field of a vector space

= Underlying field of the vector space
{synonym}

Every vector space is defined over a <field (mathematics)>.

E.g. in $\R^3$, the underlying <field (mathematics)> is $\R$, the <real numbers>. And in $\C^2$ the underlying field is $\C$, the <complex numbers>.

Any field can be used, including <finite field>. But the underlying thing has to be a field, because the definitions of a vector need all field properties to hold to make sense.

Elements of the underlying field of a vector space are known as <scalar (mathematics)>.