Linear combination

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Flesh out with a bigger see also section. Find some more references and add some comments about why this is important (linear independence)

Definition

Let $(V,\mathcal{K})$ be a vector space and let $v_1,v_2,\ldots,v_n\in V$ be given. A linear combination of $v_1,\ldots,v_n$ is any vector of the form:

• $$\sum_{i=1}^na_iv_i$$ for some scalars, $a_1,a_2,\ldots,a_n\in\mathcal{K}$.

Note: A linear combination is always a finite sum

See also

• Span
• Linear independence and dependence
• Basis