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Positive Principal Minor Property of Linear Transformations on Euclidean Jordan Algebras

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  • J. Tao

    (Loyola College in Maryland)

Abstract

In this article, we study the positive principal minor (PPM) property of linear transformations on Euclidean Jordan algebras. Specifically, we give a characterization of the PPM property on the Lorentz space ℒ n and show that the PPM property implies the Q property. We also study a matrix-induced transformation on ℒ n .

Suggested Citation

  • J. Tao, 2009. "Positive Principal Minor Property of Linear Transformations on Euclidean Jordan Algebras," Journal of Optimization Theory and Applications, Springer, vol. 140(1), pages 131-152, January.
    • Handle: RePEc:spr:joptap:v:140:y:2009:i:1:d:10.1007_s10957-008-9436-9
    DOI: 10.1007/s10957-008-9436-9
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    References listed on IDEAS

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    1. M. Seetharama Gowda & Roman Sznajder, 2006. "Automorphism Invariance of P - and GUS -Properties of Linear Transformations on Euclidean Jordan Algebras," Mathematics of Operations Research, INFORMS, vol. 31(1), pages 109-123, February.
    2. M. Seetharama Gowda & Jong-Shi Pang, 1992. "On Solution Stability of the Linear Complementarity Problem," Mathematics of Operations Research, INFORMS, vol. 17(1), pages 77-83, February.
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    Cited by:

    1. J. Tao, 2010. "Strict Semimonotonicity Property of Linear Transformations on Euclidean Jordan Algebras," Journal of Optimization Theory and Applications, Springer, vol. 144(3), pages 575-596, March.

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