Definition:Ordered Basis

Definition
Let $R$ be a ring with unity.

Let $G$ be a free $R$-module.

An ordered basis of $G$ is a sequence $\sequence {a_k}_{1 \mathop \le k \mathop \le n}$ of elements of $G$ such that $\set {a_1, \ldots, a_n}$ is a basis of $G$.

Also see

 * Definition:Change of Basis Matrix
 * Definition:Coordinate System