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 |

Definition D1405

Vector space isomorphism

Formulation 0

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

Let $V$ and $W$ each be a D29: Vector space over $R$.

A D18: Map $f : V \to W$ is

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

(2) | $f$ is a D468: Bijective map |