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 |

▾ Set of symbols

▾ Alphabet

▾ Deduction system

▾ Theory

▾ Zermelo-Fraenkel set theory

▾ Set

▾ Binary cartesian set product

▾ Binary relation

▾ Map

▾ Operation

▾ N-operation

▾ Binary operation

▾ Enclosed binary operation

▾ Groupoid

▾ Ringoid

▾ Semiring

▾ Ring

▾ Left ring action

▾ Module

▾ Linear combination

▾ Linear map

▾ Alphabet

▾ Deduction system

▾ Theory

▾ Zermelo-Fraenkel set theory

▾ Set

▾ Binary cartesian set product

▾ Binary relation

▾ Map

▾ Operation

▾ N-operation

▾ Binary operation

▾ Enclosed binary operation

▾ Groupoid

▾ Ringoid

▾ Semiring

▾ Ring

▾ Left ring action

▾ Module

▾ Linear combination

▾ Linear map

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 |