Editing Linear combination (section)

{{Short description|Sum of terms, each multiplied with a scalar}}{{Redirects|Superposition|3=superposition (disambiguation)}}
[[File:Linjcomb.png|thumb|300x300px|<math>\mathbf v </math> is the linear combination of vectors <math>\mathbf u_1 </math> and <math>\mathbf u_2 </math> such that <math>\mathbf v = 2 \cdot \mathbf u_1 + 1.5 \cdot \mathbf u_2 </math>]]
In [[mathematics]], a '''linear combination''' or '''superposition''' is an [[Expression (mathematics)|expression]] constructed from a [[Set (mathematics)|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).<ref>{{Harvard citation text|Strang|2016}} p. 3, § 1.1</ref><ref>{{Harvard citation text|Lay|Lay|McDonald|2016}} p. 28, ch. 1</ref><ref>{{Harvard citation text|Axler|2015}} p. 28, § 2.3</ref><ref>{{Harvard citation text|nLab|2015}} Linear combinations.</ref> 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 (mathematics)|field]], with some generalizations given at the end of the article.