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Linear combination

In [mathematics] , ** linear combinations ** is a concept central to [linear algebra] and related fields of mathematics.

Most of this article deals with linear combinations in the context of a [vector space] over a [field] , with some generalizations given at the end of the article.

** Definition **

Suppose that * K * is a field and * V * is a vector space over * K * . As usual, we call elements of * V * [vector] * s * and call elements of * K * [scalars] .

If * v * 1,..., * v * ** n **

:a_1 v_1 a_2 v_2 a_3 v_3 \cdots a_n v_n. \,

There is some ambiguity in the use of the term "linear combination" as to whether it refers to the expression or to its value. In most cases the value is meant, like in the assertion "the set of all linear combinations of

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