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Matrix differential calculus with applications to simple, Hadamard, and Kronecker products

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  • Magnus, J.R.

    (Tilburg University, School of Economics and Management)

  • Neudecker, H.

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Suggested Citation

  • 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.
  • Handle: RePEc:tiu:tiutis:1b2f1740-bfd1-4ea5-986c-92a680318711
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    Cited by:

    1. de Vries, Charlotte & Desharnais, Robert A. & Caswell, Hal, 2020. "A matrix model for density-dependent selection in stage-classified populations, with application to pesticide resistance in Tribolium," Ecological Modelling, Elsevier, vol. 416(C).
    2. Anat Bracha & Donald Brown, 2013. "(Ir)rational Exuberance: Optimism, Ambiguity, and Risk," Levine's Working Paper Archive 786969000000000782, David K. Levine.
    3. Alyson Raalte & Hal Caswell, 2013. "Perturbation Analysis of Indices of Lifespan Variability," Demography, Springer;Population Association of America (PAA), vol. 50(5), pages 1615-1640, October.
    4. Bruno Scalzo Dees, 2019. "Analysing Global Fixed Income Markets with Tensors," Papers 1908.02101, arXiv.org, revised Dec 2019.
    5. 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.
    6. Caro-Lopera, Francisco J. & Leiva, Víctor & Balakrishnan, N., 2012. "Connection between the Hadamard and matrix products with an application to matrix-variate Birnbaum-Saunders distributions," Journal of Multivariate Analysis, Elsevier, vol. 104(1), pages 126-139, February.
    7. Hal Caswell & Nora Sánchez Gassen, 2015. "The sensitivity analysis of population projections," Demographic Research, Max Planck Institute for Demographic Research, Rostock, Germany, vol. 33(28), pages 801-840.
    8. van Daalen, Silke & Caswell, Hal, 2020. "Variance as a life history outcome: Sensitivity analysis of the contributions of stochasticity and heterogeneity," Ecological Modelling, Elsevier, vol. 417(C).
    9. Liu, Shuangzhe & Leiva, Víctor & Zhuang, Dan & Ma, Tiefeng & Figueroa-Zúñiga, Jorge I., 2022. "Matrix differential calculus with applications in the multivariate linear model and its diagnostics," Journal of Multivariate Analysis, Elsevier, vol. 188(C).
    10. Kano, Yutaka, 1998. "More Higher-Order Efficiency: Concentration Probability," Journal of Multivariate Analysis, Elsevier, vol. 67(2), pages 349-366, November.
    11. Magnus, Jan R., 2010. "On the concept of matrix derivative," Journal of Multivariate Analysis, Elsevier, vol. 101(9), pages 2200-2206, October.
    12. Maria Gamboa & Maria Jesus Lopez-Herrero, 2020. "The Effect of Setting a Warning Vaccination Level on a Stochastic SIVS Model with Imperfect Vaccine," Mathematics, MDPI, vol. 8(7), pages 1-23, July.
    13. Mardi Dungey & John Harvey & Pierre Siklos & Vladimir Volkov, 2017. "Signed spillover effects building on historical decompositions," CAMA Working Papers 2017-52, Centre for Applied Macroeconomic Analysis, Crawford School of Public Policy, The Australian National University.
    14. M. D. Braga & C. R. Nava & M. G. Zoia, 2023. "Kurtosis-based risk parity: methodology and portfolio effects," Quantitative Finance, Taylor & Francis Journals, vol. 23(3), pages 453-469, March.
    15. Anat Bracha & Donald J. Brown, 2013. "Keynesian Utilities: Bulls and Bears," Cowles Foundation Discussion Papers 1891, Cowles Foundation for Research in Economics, Yale University.
    16. Caswell, Hal & Shyu, Esther, 2012. "Sensitivity analysis of periodic matrix population models," Theoretical Population Biology, Elsevier, vol. 82(4), pages 329-339.
    17. Braga, Maria Debora & Nava, Consuelo Rubina & Zoia, Maria Grazia, 2023. "Kurtosis-based vs volatility-based asset allocation strategies: Do they share the same properties? A first empirical investigation," Finance Research Letters, Elsevier, vol. 54(C).

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