Basis Vector

A Vector that an element of a Basis for a Vector Space, which is a Set of Linearly Indepedent whose Linear Combinations can represent any vector in that space.

Standard Basis Vector

Standard basis vectors in ${\mathbb{R}}^n$ that have a one entry for each dimension, and zeros for the rest,

• e.g. for ${\mathbb{R}}^3$: $\overrightarrow{e_1},\overrightarrow{e_2},\overrightarrow{e_3}=\hat{i},\hat{j},\hat{k}$
• You could choose any basis for ${\mathbb{R}}^n$ so long as it is linearly independent, but the standard basis for a dimension is the most convienient one