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Matrix Realization of a Homogeneous Hessian Domain

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Geometric Science of Information (GSI 2017)

Part of the book series: Lecture Notes in Computer Science ((LNIP,volume 10589))

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Abstract

Extending previous results about matrix realization of a homogeneous cone by the author, we realize any homogeneous Hessian domain as a set of symmetric matrices with a specific block decomposition. A global potential function as well as a transitive affine group action preserving the Hessian structure is also expressed in terms of the matrix realization.

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Author information

Authors and Affiliations

  1. Graduate School of Mathematics, Nagoya University, Furo-cho, Nagoya, 464-8602, Japan

    Hideyuki Ishi

  2. JST, PRESTO, 4-1-8, Honcho, Kawaguchi, 332-0012, Japan

    Hideyuki Ishi

Authors
  1. Hideyuki Ishi
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Correspondence to Hideyuki Ishi .

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Editors and Affiliations

  1. Ecole Polytechnique, Palaiseau, France

    Frank Nielsen

  2. Thales Land and Air Systems, Limours, France

    Frédéric Barbaresco

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Ishi, H. (2017). Matrix Realization of a Homogeneous Hessian Domain. In: Nielsen, F., Barbaresco, F. (eds) Geometric Science of Information. GSI 2017. Lecture Notes in Computer Science(), vol 10589. Springer, Cham. https://doi.org/10.1007/978-3-319-68445-1_23

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  • DOI: https://doi.org/10.1007/978-3-319-68445-1_23

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-68444-4

  • Online ISBN: 978-3-319-68445-1

  • eBook Packages: Computer ScienceComputer Science (R0)

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