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A gentle introduction to matrix calculus

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  • Magnus, Jan R.

Abstract

Matrix calculus is an important tool when we wish to optimize functions involving matrices or perform sensitivity analyses. This tutorial is designed to make matrix calculus more accessible to graduate students and young researchers. It contains the theory that would suffice in most applications, many fully worked-out exercises and examples, and presents some of the ‘tacit knowledge’ that is prevalent in this field.

Suggested Citation

  • Magnus, Jan R., 2024. "A gentle introduction to matrix calculus," Journal of Econometrics, Elsevier, vol. 244(1).
    • Handle: RePEc:eee:econom:v:244:y:2024:i:1:s0304407624002070
    DOI: 10.1016/j.jeconom.2024.105862
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    References listed on IDEAS

    as
    1. Carl Eckart & Gale Young, 1936. "The approximation of one matrix by another of lower rank," Psychometrika, Springer;The Psychometric Society, vol. 1(3), pages 211-218, September.
    2. Masako Ikefuji & Roger J. A. Laeven & Jan R. Magnus & Yuan Yue, 2022. "Earthquake Risk Embedded in Property Prices: Evidence From Five Japanese Cities," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 117(537), pages 82-93, January.
    3. Magnus, Jan R., 2010. "On the concept of matrix derivative," Journal of Multivariate Analysis, Elsevier, vol. 101(9), pages 2200-2206, October.
    Full references (including those not matched with items on IDEAS)

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    More about this item

    Keywords

    Differential calculus; Multivariate; Optimization; Vec operator; Commutation matrix;
    All these keywords.

    JEL classification:

    • C02 - Mathematical and Quantitative Methods - - General - - - Mathematical Economics
    • C60 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - General
    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis

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