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On the use of coordinate-free matrix calculus

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  • Brinkhuis, Jan

Abstract

For a standard tool in econometrics, matrix calculus, an approach is illustrated in this note that is unusual in that context, a coordinate-free approach. It can help to eliminate the persistent use of non-standard conventions. The Kronecker product and its use can be better understood. The complications and pitfalls of defining twice differentiability by partial derivatives are avoided. Its use is demonstrated, for example by giving a coordinate-free determination of the derivative of the determinant.

Suggested Citation

  • Brinkhuis, Jan, 2015. "On the use of coordinate-free matrix calculus," Journal of Multivariate Analysis, Elsevier, vol. 133(C), pages 377-381.
    • Handle: RePEc:eee:jmvana:v:133:y:2015:i:c:p:377-381
    DOI: 10.1016/j.jmva.2014.09.019
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    References listed on IDEAS

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    1. Sturm, Jos F. & Zhang, Shuzhong, 2000. "On weighted centers for semidefinite programming," European Journal of Operational Research, Elsevier, vol. 126(2), pages 391-407, October.
    2. Magnus, Jan R., 2010. "On the concept of matrix derivative," Journal of Multivariate Analysis, Elsevier, vol. 101(9), pages 2200-2206, October.
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    Cited by:

    1. 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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