# Linear combination

## Sum of terms, each multiplied with a scalar / From Wikipedia, the free encyclopedia

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In mathematics, a **linear combination** is an expression constructed from a set of terms by multiplying each term by a constant and adding the results (e.g. a linear combination of *x* and *y* would be any expression of the form *ax* + *by*, where *a* and *b* are constants).^{[1]}^{[2]}^{[3]}^{[4]} The concept of linear combinations is 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.