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Baha Alzalg (baha2mathgmail.com) Abstract: In this paper, we study and analyze the algebraic structure of the circular cone. We establish a new efficient spectral decomposition, set up the Jordan algebra associated with the circular cone, and prove that this algebra forms a Euclidean Jordan algebra with a certain inner product. We then show that the cone of squares of this Euclidean Jordan algebra is indeed the circular cone itself. The circular cones form a much more general class than the secondorder cones, so we generalize some important algebraic properties in the Euclidean Jordan algebra of the secondorder cones to the Euclidean Jordan algebra of the circular cones. Keywords: Jordan algebras; Euclidean Jordan algebras; Symmetric cones; Circular cones; Secondorder cones Category 1: Linear, Cone and Semidefinite Programming Category 2: Linear, Cone and Semidefinite Programming (SecondOrder Cone Programming ) Citation: Download: [PDF] Entry Submitted: 07/15/2015 Modify/Update this entry  
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