Loterre: Mathématiques: convex cone

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convex cone

In linear algebra, a cone—sometimes called a linear cone for distinguishing it from other sorts of cones—is a subset of a vector space that is closed under positive scalar multiplication; that is, $C$ is a cone if ${\\displaystyle x\\in C}$ implies ${\\displaystyle sx\\in C}$ for every positive scalar $s$ . When the scalars are real numbers, or belong to an ordered field, one generally calls a cone a subset of a vector space that is closed under multiplication by a positive scalar. In this context, a convex cone is a cone that is closed under addition, or, equivalently, a subset of a vector space that is closed under linear combinations with positive coefficients. It follows that convex cones are convex sets.
(Wikipedia, The Free Encyclopedia, https://en.wikipedia.org/wiki/Convex_cone)

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