Rational-linear map
= Rational-linear map
{title2=$f(qx)=qf(x)\quad(q\in\mathbb Q)$}
A <rational-linear map> is a <linear map> when its domain and codomain are regarded as <vector spaces> over the <rational numbers>. An additive map on a rational <vector subspace> of the <real numbers> is automatically rational-linear: <integer> homogeneity follows by repeated <addition>, and division by a positive <integer> gives <rational homogeneity of an additive function>.