By definition, I know that a convex cone is both a convex set and a cone. How do I prove that U is a convex cone iff:

$\displaystyle x \in U, y \in U, a \ge 0, b \ge 0 \implies ax+by \in U $

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- Jan 12th 2010, 12:33 PMaltave86Convex cone
By definition, I know that a convex cone is both a convex set and a cone. How do I prove that U is a convex cone iff:

$\displaystyle x \in U, y \in U, a \ge 0, b \ge 0 \implies ax+by \in U $