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Article Navigation> JOURNAL OF BEIJING INSTITUTE OF TECHNOLOGY> 2009> 18(4): 484-487
ZHANG Shi-cheng, SUN Hua-fei, LI Chun-hui. Information Geometry of Positive Definite Matrices[J]. JOURNAL OF BEIJING INSTITUTE OF TECHNOLOGY, 2009, 18(4): 484-487.
Citation: ZHANG Shi-cheng, SUN Hua-fei, LI Chun-hui. Information Geometry of Positive Definite Matrices[J].JOURNAL OF BEIJING INSTITUTE OF TECHNOLOGY, 2009, 18(4): 484-487.
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Information Geometry of Positive Definite Matrices

  • School of Science, Beijing Institute of Technology, Beijing 100081, China;School of Mathematics, Xuzhou Normal University, Xuzhou, Jiangsu 221116, China

  • Received Date:2009-01-16
    Abstract
  • A new Riemannian metric for positive definite matrices is defined and its geometric structures are investigated by means of dual connections introduced to statistical analysis by S. Amari. A few interesting results are obtained and some of those obtained by other authors are extended in our research.
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    • References (6)
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    Zhong F W, Sun H F. Geometric structures of stable time-variant state feedback systems[J]. Journal of Beijing Institute of Technology, 2007, 16(4):500-504.
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    Hill R D. On the cone of positive semidefinite matrics[J]. Linear Algebra Appl, 1987, 90(2):81-88.
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    Ohara A, Suda N, Amari S. Dualistic differential geometry of positive definite matrics and its applications to related problems[J]. Linear Algebra Appl, 1996, 247(1):31-53.
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    Ohara A, Amari S. Differential geometry structures of stable feedback systems with dual connections[J]. Kybernetika, 1994, 30(2):369-386.
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    Amari S. Methods of information geometry[M]. Oxford: Oxford University Press, 2000.
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    Amari S. Differential geometry methods in statistics, lecture notes in statistics[M]. New York: Spring-Verlag, 1985. (Edited by
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