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On the concept of matrix derivative

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  • Magnus, Jan R.

Abstract

We discuss how to generalize the concept of vector derivative to matrix derivative, propose two definitions, a 'broad' and a 'narrow' one, compare the two definitions, and argue in favor of the narrow definition.

Suggested Citation

  • Magnus, Jan R., 2010. "On the concept of matrix derivative," Journal of Multivariate Analysis, Elsevier, vol. 101(9), pages 2200-2206, October.
    • Handle: RePEc:eee:jmvana:v:101:y:2010:i:9:p:2200-2206
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    References listed on IDEAS

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    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.
    2. Robert Boik, 2008. "Newton Algorithms for Analytic Rotation: an Implicit Function Approach," Psychometrika, Springer;The Psychometric Society, vol. 73(2), pages 231-259, June.
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    Cited by:

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    4. D. Stephen G. Pollock, 2021. "Multidimensional Arrays, Indices and Kronecker Products," Econometrics, MDPI, vol. 9(2), pages 1-15, April.
    5. Stephen Pollock, 2011. "On Kronecker Products, Tensor Products And Matrix Differential Calculus," Discussion Papers in Economics 11/34, Division of Economics, School of Business, University of Leicester, revised Jul 2011.
    6. Mutschler, Willi, 2015. "Identification of DSGE models—The effect of higher-order approximation and pruning," Journal of Economic Dynamics and Control, Elsevier, vol. 56(C), pages 34-54.
    7. 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).
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    10. Richard M. Golden & Steven S. Henley & Halbert White & T. Michael Kashner, 2016. "Generalized Information Matrix Tests for Detecting Model Misspecification," Econometrics, MDPI, vol. 4(4), pages 1-24, November.

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