Definition – Linear combination (of a finite set).

Definition

Consider a vector space $V$ over $F$ . Let $R$ be a subset of $F$ with $|R| = n$ . Let $E$ be a subset of $V$ with $|E| = n$ . Let $e_i\in{E}$ and $r_i\in{R}$ . A linear combination of the vectors in $E$ is defined as

$\sum\limits_{i=1}^{n} r_i e_i = r_1 e_1 + r_2 e_2 + ... + r_n e_n$

Notes