Definition:Standard Basis

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

Let $\sequence {e_k}_{1 \mathop \le k \mathop \le n}$ be the standard ordered basis of the $R$-module $R^n$.

The corresponding (unordered) set $\set {e_1, e_2, \ldots, e_n}$ 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)