Conical combination
![In the plane, the conical hull of a circle passing through the origin is the open half-plane defined by the tangent line to the circle at the origin plus the origin.](/Images/godic/202501/30/Circle-conic-hull.svg1128.png")
Given a finite number of vectors ![x_1, x_2, \dots, x_n\,](/Images/godic/202501/30/162e2e99f5d2f92ee0cd7194632d7e411128.png")
in a real vector space, a conical combination, conical sum, or weighted sum of these vectors is a vector of the form
where the real numbers ![\alpha_i\,](/Images/godic/202501/30/28f96e814bd493d6d461037c95d61e6b1128.png")
satisfy ![\alpha_i\ge 0.](/Images/godic/202501/30/42d4f2cefb7d6163187564078af36cf61128.png")
The name derives from the fact that a conical sum of vectors defines a cone (possibly in a lower-dimensional subspace).