The set of all possible [linear combinations](Linear%20Algebra%20and%20Matrix%20Theory%20(index).md#linear%20combinations) that can be written given a list of [vectors](Linear%20Algebra%20and%20Matrix%20Theory%20(index).md#Vectors) $(v_1,...,v_m)$ is the _linear span_ or simply _span_ and is denoted as $\mathrm{span}(v_1,...,v_m)=\{a_1v_1+...+a_mv_m;a_1,...,a_m \in \mathbb{F}\}$ # Finite dimensional vector spaces  %%please connect this to vector spaces. is there a span for infinite dimensional vector spaces as well? Check this%% %%At some point please verify the following: That the span of any list of vectors in V is a sub-space of V.%% #MathematicalFoundations/Algebra/AbstractAlgebra/LinearAlgebra #MathematicalFoundations/Algebra/AbstractAlgebra/LinearAlgebra/VectorSpaces