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.

Given a finite number of vectors $x_1, x_2, \dots, x_n\,$ 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 $\alpha_i\,$ satisfy $\alpha_i\ge 0.$

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

单词	Nonnegative combination
释义	Nonnegative combination 英语百科 Conical combination Given a finite number of vectors $x_1, x_2, \dots, x_n\,$ 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 $\alpha_i\,$ satisfy $\alpha_i\ge 0.$ The name derives from the fact that a conical sum of vectors defines a cone (possibly in a lower-dimensional subspace).
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Nonnegative combination

Conical combination