Vector space/Linear combination/Definition

Linear combination

Let ${}K$ be a field, and let ${}V$ be a ${}K$-vector space. Let ${}v_{1},\ldots ,v_{n}$ denote a family of vectors in ${}V$. Then the vector

$s_{1}v_{1}+s_{2}v_{2}+\cdots +s_{n}v_{n}{\text{ with }}s_{i}\in K$

is called a linear combination of this vectors (for the coefficient tuple ${}(s_{1},\ldots ,s_{n})$).