Linear combination

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Definition

Let [ilmath](V,\mathcal{K})[/ilmath] be a vector space and let [ilmath]v_1,v_2,\ldots,v_n\in V[/ilmath] be given. A linear combination of [ilmath]v_1,\ldots,v_n[/ilmath] is any vector of the form[1]:

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

Note: A linear combination is always a finite sum[1][Note 2]