Non-negative Linear Span of Vectors

Question

I would like to understand if there is a common concept of a `linear span' of a set of vectors which are combined with non-negative multipliers.

I know that usual definition of the span of a set of vectors as follows [wiki]:

$\operatorname{span}(S) = \left \{ {\sum_{i=1}^k \lambda_i v_i \Big| k \in \mathbb{N}, v_i \in S, \lambda _i \in \mathbf{K}} \right \}.$

Is there a commonly used name for a span when $\lambda _i \in R^+$ (positive real numbers) so that I can study this further? I cannot find much material in this area.

Ultimately, I am interested if there is a way to distinguish between matrices (or collections of vectors) that have full rank even if only positive multipliers are permitted.

Thanks for any guidance.

Answer 1

What you have is a convex cone.

A cone is a set closed under positive scaling. A convex cone is a cone which is also closed under convex combinations.