Given a set $\{f_{1},\ldots,f_{k}\}$ of maps $\mathbb{R}^{n}\rightarrow \mathbb{R}^{m}$ how is it usually defined the notion of linear (in)dependence among them? (Is it the same as for single variable real valued functions?).
Does the notion of linear (in)dependence have an analog, or a generalization to maps between more general types of spaces? (e.g. maps between Banach or Hilbert spaces, or even metric spaces)