Definition:Basis (Linear Algebra)

Module
Let $\left({G, +_G, \circ}\right)_R$ be a unitary $R$-module.

A basis of $G$ (plural: bases) is a linearly independent subset of $G$ which is a generator for $G$.

Comment
The pronunciation of bases in this context is bay-seez, not bay-siz.

Also see

 * Expression of Vector as Linear Combination from Basis is Unique