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Matrix Realization of a Homogeneous Cone

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Book cover Geometric Science of Information (GSI 2015)

Part of the book series: Lecture Notes in Computer Science ((LNIP,volume 9389))

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Abstract

Based on the theory of compact normal left-symmetric algebra (clan), we realize every homogeneous cone as a set of positive definite real symmetric matrices, where homogeneous Hessian metrics as well as a transitive group action on the cone are described efficiently.

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Author information

Authors and Affiliations

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

    Hideyuki Ishi

Authors
  1. Hideyuki Ishi
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Correspondence to Hideyuki Ishi .

Editor information

Editors and Affiliations

  1. Bâtiment Alan Turing, CS35003, École Polytechnique, Palaiseau, France

    Frank Nielsen

  2. Thales Land\& Air Systems, Limours, France

    Frédéric Barbaresco

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Ishi, H. (2015). Matrix Realization of a Homogeneous Cone. In: Nielsen, F., Barbaresco, F. (eds) Geometric Science of Information. GSI 2015. Lecture Notes in Computer Science(), vol 9389. Springer, Cham. https://doi.org/10.1007/978-3-319-25040-3_28

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  • DOI: https://doi.org/10.1007/978-3-319-25040-3_28

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-25039-7

  • Online ISBN: 978-3-319-25040-3

  • eBook Packages: Computer ScienceComputer Science (R0)

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