Let K {\displaystyle {}K} be a field, and let V {\displaystyle {}V} be a K {\displaystyle {}K} -vector space. Then a linearly independent generating system v i ∈ V {\displaystyle {}v_{i}\in V} , i ∈ I {\displaystyle {}i\in I} , of V {\displaystyle {}V} is called a basis of V {\displaystyle {}V} .
