Finite - Dimensional Cones 1 1 Basic Definitions
نویسنده
چکیده
Example 1. The set R+ is a closed, convex, pointed cone. The half plane {x ∈ R2 : x2 ≥ 0} is a closed, convex cone that is not pointed. The union of the open half plane {x ∈ R2 : x2 > 0} and 0 is a somewhat pathological example of a convex cone that is pointed but not closed. Remark 1. There are several different definitions of “cone” in the mathematics. Some, for example, require the cone to be convex but allow the cone to omit the origin. The definition used here is sometimes referred to as the linear algebra definition.
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