Let
\[F\]
be a set of functions operating on a domain \[D\]
, which send each element of \[D\]
into a codomain \[C\]
, and let \[x \in D\]
. The set of all functions operating on \[x\]
defines a vector space \[V\]
aince1.
\[\mathbf{0}(x)=0 \in \mathbf{V}\]
2. For
\[f,g \in \mathbf{V}, a,b \in \mathbb{R},af(x)+bg(x)=(af+bg)(x) \rightarrow af+bg \in \mathbf{V}\]