linear combination
a linear combination of a list 
of vectors in 
is a vector of the form
where 
.
[cite:;taken from @algebra_axler_2024 definition 2.2 linear combination]
of vectors in is a vector of the formwhere .[cite:;taken from @algebra_axler_2024 definition 2.2 linear combination]
let 
be a vector space, let 
and 
, then 
is a linear combination of elements of 
although the term linear combination is somewhat ambiguous as it can refer to either the combination of vectors and coefficients itself or (in most cases) to its value, i.e.
means the vector 
is a linear combination of the vectors in the set
be a vector space, let and , then is a linear combination of elements of although the term linear combination is somewhat ambiguous as it can refer to either the combination of vectors and coefficients itself or (in most cases) to its value, i.e.
means the vector is a linear combination of the vectors in the set