Dual cone and polar cone: Difference between revisions

Revision as of 19:52, 14 March 2012

Revision as of 17:54, 18 March 2012

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The '''dual cone''' <math>C^* </math> of a [[subset]] <math>C</math> in a [[linear space]] <math>X</math>, e.g. [[Euclidean space]] <math>\mathbb R^n</math>, with [[topological]] [[dual space]] <math>X^*</math> is the set

:<math>C^* = \left \{y\in \mathbb X^*: \langle y , x \rangle \geq 0 \quad \forall x\in C \right \},</math>

<math>C^* </math> is always a [[convex cone]], even if <math>C </math> is neither [[convex set|convex]] nor a [[linear cone|cone]].