ThmDex – An index of mathematical definitions, results, and conjectures.
Set of symbols
Alphabet
Deduction system
Theory
Zermelo-Fraenkel set theory
Set
Binary cartesian set product
Binary relation
Map
Empty map
Collection
Ring element collection
Ring element combination
Formal linear combination
Standard formal linear combination
Set of standard formal linear combinations
Linearly independent set
Module basis
Vector space basis
Definition D174
Vector space dimension
Formulation 1
Let $R$ be a D273: Division ring such that
(i) $V$ is a D29: Vector space over $R$
(ii) $B$ is a D173: Vector space basis for $V$ over $R$
The dimension of $V$ over $R$ is the D15: Set cardinality \begin{equation} \text{dim}_R(V) : = |B| \end{equation}