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