Let \(V\) be a vector space over a field \(F\). Consider finitely many vectors \(x_1,\ldots,x_n\in V\) and finitely many field elements \(\alpha_1,\ldots,\alpha_n\in F\). Then the vector \(y\in V\) with
\[y:=\alpha_1 x_1 + \ldots \alpha_n x_n\] is called the linear combination of the vectors \(x_1,\ldots,x_n\in V\).
Definitions: 1 2 3 4
Lemmas: 5
Proofs: 6