Partial Order Defined By A Convex Cone
A pointed and salient convex cone C induces a partial ordering "≤" on V, defined so that x≤y if and only if y − x C. (If the cone is flat, the same definition gives merely a preorder.) Sums and positive scalar multiples of valid inequalities with respect to this order remain valid inequalities. A vector space with such an order is called an ordered vector space. Examples include the product order on real-valued vectors and the Loewner order on matrices.
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