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Multidimensional Arrays, Indices and Kronecker Products

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  • D. Stephen G. Pollock

    (Department of Economics, University of Leciceter, Leciceter LE1 7RH, UK)

Abstract

Much of the algebra that is associated with the Kronecker product of matrices has been rendered in the conventional notation of matrix algebra, which conceals the essential structures of the objects of the analysis. This makes it difficult to establish even the most salient of the results. The problems can be greatly alleviated by adopting an orderly index notation that reveals these structures. This claim is demonstrated by considering a problem that several authors have already addressed without producing a widely accepted solution.

Suggested Citation

  • D. Stephen G. Pollock, 2021. "Multidimensional Arrays, Indices and Kronecker Products," Econometrics, MDPI, vol. 9(2), pages 1-15, April.
    • Handle: RePEc:gam:jecnmx:v:9:y:2021:i:2:p:18-:d:545552
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    References listed on IDEAS

    as
    1. Turkington,Darrell A., 2002. "Matrix Calculus and Zero-One Matrices," Cambridge Books, Cambridge University Press, number 9780521807883.
    2. Magnus, Jan R., 2010. "On the concept of matrix derivative," Journal of Multivariate Analysis, Elsevier, vol. 101(9), pages 2200-2206, October.
    3. Magnus, J.R. & Neudecker, H., 1979. "The commutation matrix : Some properties and applications," Other publications TiSEM d0b1e779-7795-4676-ac98-1, Tilburg University, School of Economics and Management.
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