Definition:Standard Basis

Definition
Let $\left({R, +, \circ}\right)$ be a ring with unity whose zero is $0_R$ and whose unity is $1_R$.

Let $\left \langle {e_k} \right \rangle_{1 \mathop \le k \mathop \le n}$ be the standard ordered basis of the $R$-module $R^n$.

The corresponding (unordered) set $\left\{{e_1, e_2, \ldots, e_n}\right\}$ is called the standard basis of $R^n$.

Vector Space
The concept of a standard basis is often found in the context of vector spaces.

Also see

 * Definition:Standard Ordered Basis
 * Definition:Basis (Linear Algebra)