• Journal of applied mathematics & informatics
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• 제34권3_4호
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• pp.309-317
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• 2016

Let V be a Euclidean Jordan algebra with a symmetric cone K. We show that for a Z-transformation L with the additional property L(K) ⊆ K (which we will call ’cone-preserving’), GUS ⇔ strictly copositive on K ⇔ monotone + P. Specializing the result to the Stein transformation S_A(X) := X - AXA^T on the space of real symmetric matrices with the property $S_A(S^n_+){\subseteq}S^n_+$, we deduce that S_A GUS ⇔ I ± A positive definite.

• 대한수학회지
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• 제43권3호
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• pp.507-528
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• 2006

In this paper we show that the Koecher's Jordan automorphic generators of one variable on an irreducible symmetric cone are enough to determine the elements of scalar multiple of the Jordan identity on the attached simple Euclidean Jordan algebra. Its various geometric, Jordan and Lie theoretic interpretations associated to the Cartan-Hadamard metric and Cartan decomposition of the linear automorphisms group of a symmetric cone are given with validity on infinite-dimensional spin factors

• Korean Journal of Mathematics
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• 제31권4호
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• pp.495-504
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• 2023

This article deals with non-degenerate linear transformations on Euclidean Jordan algebras. First, we study non-degenerate for cone invariant, copositive, Lyapunov-like, and relaxation transformations. Further, we study that the non-degenerate is invariant under principal pivotal transformations and algebraic automorphisms.

• Nonlinear Functional Analysis and Applications
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• 제26권4호
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• pp.649-662
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• 2021

Recently the author studied a one-parameter family of divergences and considered the related median minimization problem of finite points over these divergences in general symmetric cones. In this article, to utilize the results practically, we deal with a special symmetric cone called second order cone, which is important in optimization fields. To be more specific, concrete computations of divergences with its gradients and the unique minimizer of the median minimization problem of two points are provided skillfully.