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A Representation Theorem For Lyapunov-Like Transformations On Euclidean Jordan Algebras

Author

Listed:
  • JIYUAN TAO

    (Department of Mathematics and Statistics, Loyola University Maryland, Baltimore, Maryland 21210, USA)

  • M. SEETHARAMA GOWDA

    (Department of Mathematics and Statistics, University of Maryland, Baltimore County, Baltimore, Maryland 21250, USA)

Abstract

A Lyapunov-like (linear) transformationLon a Euclidean Jordan algebraVis defined by the condition$$x \in K,\enspace y\in K^*,\quad \langle x,y\rangle =0\Rightarrow \langle L(x),y\rangle=0,$$whereKis the symmetric cone ofV. In this paper, we give an elementary proof (avoiding Lie algebraic ideas and results) of the fact that Lyapunov-like transformations onVare of the formLa+ D, wherea ∈ V,Dis a derivation, andLa(x) = a ◦ xfor allx ∈ V.

Suggested Citation

  • Jiyuan Tao & M. Seetharama Gowda, 2013. "A Representation Theorem For Lyapunov-Like Transformations On Euclidean Jordan Algebras," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 15(04), pages 1-11.
    • Handle: RePEc:wsi:igtrxx:v:15:y:2013:i:04:n:s0219198913400343
    DOI: 10.1142/S0219198913400343
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    Cited by:

    1. Roman Sznajder, 2016. "The Lyapunov rank of extended second order cones," Journal of Global Optimization, Springer, vol. 66(3), pages 585-593, November.

    More about this item

    Keywords

    Euclidean Jordan algebra; symmetric cone; Zand Lyapunov-like transformations; 90C33; 17C55; 15A48;
    All these keywords.

    JEL classification:

    • B4 - Schools of Economic Thought and Methodology - - Economic Methodology
    • C0 - Mathematical and Quantitative Methods - - General
    • C6 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling
    • C7 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory
    • D5 - Microeconomics - - General Equilibrium and Disequilibrium
    • D7 - Microeconomics - - Analysis of Collective Decision-Making
    • M2 - Business Administration and Business Economics; Marketing; Accounting; Personnel Economics - - Business Economics

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