Definition:Dimension (Linear Algebra)

Module
Let $$G$$ be a unitary $R$-module which has a basis of $$n$$ elements.

Then $$G$$ is said to have a dimension of $$n$$ or to be $$n$$-dimensional.

A module is finite-dimensional if it is $$n$$-dimensional for some $$n \in \mathbb{N}^*$$.

The dimension of a unitary $R$-module $$G$$ is denoted $$\dim \left({G}\right)$$.

Vector Space
Given a vector space $$V$$, the dimension of $$V$$ is the minimum number of vectors in a basis for $$V$$.