Let $R$ be a D273: Division ring.
Let $V$ and $W$ each be a D29: Vector space over $R$.
A D18: Map $f : V \to W$ is vector space isomorphism from $V$ to $W$ over $R$ if and only if

(1)	$f$ is a D690: Linear map from $V$ to $W$ over $R$
(2)	$f$ is a D468: Bijective map