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On some definitions in matrix algebra

Author

Listed:
  • Jan R. Magnus

    (Department of Econometrics & OR, Tilburg University)

  • Karim M. Abadir

    (Tanaka Business School, Imperial College London)

Abstract

Many definitions in matrix algebra are not standardized. This notediscusses some of thepitfalls associated with undesirable orwrong definitions, anddealswith central conceptslikesymmetry, orthogonality, square root, Hermitian and quadratic forms, and matrix derivatives.

Suggested Citation

  • Jan R. Magnus & Karim M. Abadir, 2007. "On some definitions in matrix algebra," CIRJE F-Series CIRJE-F-476, CIRJE, Faculty of Economics, University of Tokyo.
    • Handle: RePEc:tky:fseres:2007cf476
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    File URL: http://www.cirje.e.u-tokyo.ac.jp/research/dp/2007/2007cf476.pdf
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    References listed on IDEAS

    as
    1. Magnus, J.R. & Neudecker, H., 1985. "Matrix differential calculus with applications to simple, Hadamard, and Kronecker products," Other publications TiSEM 1b2f1740-bfd1-4ea5-986c-9, Tilburg University, School of Economics and Management.
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    Cited by:

    1. Ishihara, Tsunehiro & Omori, Yasuhiro, 2012. "Efficient Bayesian estimation of a multivariate stochastic volatility model with cross leverage and heavy-tailed errors," Computational Statistics & Data Analysis, Elsevier, vol. 56(11), pages 3674-3689.
    2. Trojan, Sebastian, 2014. "Multivariate Stochastic Volatility with Dynamic Cross Leverage," Economics Working Paper Series 1424, University of St. Gallen, School of Economics and Political Science.
    3. Ishihara, Tsunehiro & Omori, Yasuhiro & Asai, Manabu, 2016. "Matrix exponential stochastic volatility with cross leverage," Computational Statistics & Data Analysis, Elsevier, vol. 100(C), pages 331-350.

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