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). 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.