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Convex cone
Mathematical set closed under positive linear combinations / From Wikipedia, the free encyclopedia
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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 implies
for every positive scalar s. A cone need not be convex, or even look like a cone in Euclidean space.
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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.[1]
In this article, only the case of scalars in an ordered field is considered.