Conical combination

Given a finite number of vectors ${\displaystyle x_{1},x_{2},\dots ,x_{n}}$ in a real vector space, a conical combination, conical sum, or weighted sum^[1][2] of these vectors is a vector of the form

${\displaystyle \alpha _{1}x_{1}+\alpha _{2}x_{2}+\cdots +\alpha _{n}x_{n}}$

where ${\displaystyle \alpha _{i}}$ are non-negative real numbers.

The name derives from the fact that the set of all conical sum of vectors defines a cone (possibly in a lower-dimensional subspace).